The Heavy Weapon Master has trained himself to use the weight of his weapons and armor to his advantage. He eschews the frippery of light weapons and instead relies on the sciences of momentum and balance.
Improved Control
You receive +1 to hit with any heavy melee weapon.
Light On Your Feet
You receive Expertise with your Athletics Skill.
Your Jump height is increased by 2 feet and your jump distance is increased by 4 feet.
Second Skin
At 10th level, you receive the Defense Fighting Style.
In addition, as long as you are wearing Heavy Armor and not using a shield your armor will reduce incoming damage from nonmagical slashing, piercing, and bludgeoning attacks by 1 point per attack.
Precision Strikes
Starting at 15th level, your weapon attacks score a critical hit on a roll of 19–20.
You also receive a +1 to hit with heavy melee weapons.
Superhuman Endurance
At 18th level, you attain the pinnacle of resilience in battle. You gain another use of Second Wind and all of your uses of Second Wind now heal 2D10+ your Fighter level HP.
So at level 3 you get expertise with athletics, and increased jumping? Expertise is nice but the jumping feels kind of situational and lackluster. +1 to attacks is useful but...doesn't really grab me. It has no flavor. Compared to a battlemaster's manuvers, the echo knight's echo, the arcane archer's arcane shots... this just doesn't feel very exciting.
You skipped over 7th level. 10th level feels underwhelming. +1 to ac is useful but again not big on flavor. The -1 damage from attacks feels like a watered down heavy armor master, that won't make that much of a difference as you get into higher levels unless you're up against crazy big hordes of really weak enemies.
15: Champion gets this critial increase at level THREE. Getting effectively +2 to attacks now is again useful but no flavor.
18: This is pretty underwhelming as a capstone IMO.
This doesn't really give the fighter anything new to play with. I can understand wanting to make a subclass that favors heavy weapons, the way that arcane archer is a ranged/archery specific subclass. But where that has cool magic arrow stuff going on, this doesn't really have any flavor or excitement to it. I'd suggest coming up with some kind of theme to go along with using heavy weapons that inspires some subclass features that are both on par with other subclasses and also have some fun flavor to play into that theme. I don't mean to be mean but this feels lackluster mechanically and utterly devoid of interesting flavor.
Edit: A couple of possible suggestions:
Maybe have a limited number of uses of some modifications to attacks with heavy weapons.
Like the ability to smash your weapon down on an attack. When you hit an enemy with a heavy weapon, it makes a shockwave in a small cone that can damage the enemy and creatures near it. Or Something like like making them make a CON save and on a failure, they're debuffed like the crusher feat and attacks against htem have advantage temporarily. Or on a hit, having your weapon swing wide and hit a second creature etc. You wouldn't need to go a magic route like arcane archer, but having some moves that emphasize the big, heavy nature of your weapon could go a long way to make it feel more exciting.
Honestly though a lot of the ideas that come to mind on my end on this idea could already be handled by the battlemaster subclass. Like reflavoring trip attack to just pushing them down with overhwelming force. Sweeping attack to hit a second creature with your big weapon. Pushing attack to emphasize the force behind your attack. Menacing attack works well with heavy weapons I think. Battlemaster is such a versatile and great subclass that it's honestly hard for me to conceptualize new fighter subclasses that don't go a bit outside the box in other ways. This idea kind of just feels like champion but locked to one weapon type and not as good. With champion there as the 'simple' subclass and battlemaster more strategic and versatile with its manuevers, I feel other fighter subclasses kind of need something outside the box like arcane archer or echo knight to compete with them.
I don't feel like this idea really does much to emphasize the heavy weapon aspect any more than a champion that just takes the heavy weapon fighting style does already.
The Heavy Weapon Master has trained himself to use the weight of his weapons and armor to his advantage. He eschews the frippery of light weapons and instead relies on the sciences of momentum and balance.
Improved Control
You receive +1 to hit with any heavy melee weapon.
Light On Your Feet
You receive Expertise with your Athletics Skill.
Your Jump height is increased by 2 feet and your jump distance is increased by 4 feet.
Second Skin
At 10th level, you receive the Defense Fighting Style.
In addition, as long as you are wearing Heavy Armor and not using a shield your armor will reduce incoming damage from nonmagical slashing, piercing, and bludgeoning attacks by 1 point per attack.
Precision Strikes
Starting at 15th level, your weapon attacks score a critical hit on a roll of 19–20.
You also receive a +1 to hit with heavy melee weapons.
Superhuman Endurance
At 18th level, you attain the pinnacle of resilience in battle. You gain another use of Second Wind and all of your uses of Second Wind now heal 2D10+ your Fighter level HP.
Honestly this feels kind of underwhelming.
So at level 3 you get expertise with athletics, and increased jumping? Expertise is nice but the jumping feels kind of situational and lackluster. +1 to attacks is useful but...doesn't really grab me. It has no flavor. Compared to a battlemaster's manuvers, the echo knight's echo, the arcane archer's arcane shots... this just doesn't feel very exciting.
You skipped over 7th level. 10th level feels underwhelming. +1 to ac is useful but again not big on flavor. The -1 damage from attacks feels like a watered down heavy armor master, that won't make that much of a difference as you get into higher levels unless you're up against crazy big hordes of really weak enemies.
15: Champion gets this critial increase at level THREE. Getting effectively +2 to attacks now is again useful but no flavor.
18: This is pretty underwhelming as a capstone IMO.
This doesn't really give the fighter anything new to play with. I can understand wanting to make a subclass that favors heavy weapons, the way that arcane archer is a ranged/archery specific subclass. But where that has cool magic arrow stuff going on, this doesn't really have any flavor or excitement to it. I'd suggest coming up with some kind of theme to go along with using heavy weapons that inspires some subclass features that are both on par with other subclasses and also have some fun flavor to play into that theme. I don't mean to be mean but this feels lackluster mechanically and utterly devoid of interesting flavor.
Edit: A couple of possible suggestions:
Maybe have a limited number of uses of some modifications to attacks with heavy weapons.
Like the ability to smash your weapon down on an attack. When you hit an enemy with a heavy weapon, it makes a shockwave in a small cone that can damage the enemy and creatures near it. Or Something like like making them make a CON save and on a failure, they're debuffed like the crusher feat and attacks against htem have advantage temporarily. Or on a hit, having your weapon swing wide and hit a second creature etc. You wouldn't need to go a magic route like arcane archer, but having some moves that emphasize the big, heavy nature of your weapon could go a long way to make it feel more exciting.
Honestly though a lot of the ideas that come to mind on my end on this idea could already be handled by the battlemaster subclass. Like reflavoring trip attack to just pushing them down with overhwelming force. Sweeping attack to hit a second creature with your big weapon. Pushing attack to emphasize the force behind your attack. Menacing attack works well with heavy weapons I think. Battlemaster is such a versatile and great subclass that it's honestly hard for me to conceptualize new fighter subclasses that don't go a bit outside the box in other ways. This idea kind of just feels like champion but locked to one weapon type and not as good. With champion there as the 'simple' subclass and battlemaster more strategic and versatile with its manuevers, I feel other fighter subclasses kind of need something outside the box like arcane archer or echo knight to compete with them.
I don't feel like this idea really does much to emphasize the heavy weapon aspect any more than a champion that just takes the heavy weapon fighting style does already.