After many battles with your weapon and practicing in your off time you've become extra proficient with your weapon of choice. Choose a weapon that meets the prerequisites (ex. "greatsword", "club", "crossbow")

With your chosen weapon you gain +1 to attack and damage (this is different from simply being a +1 weapon as you do not deal magic damage) and your weapon gains a special ability as listed below:

Battleaxe: your battleaxe now has the helm splitter property, when you score a critical hit on your opponent their AC drops by 2 (if they're wearing a helm it splits off their head) until the battle ends or if they equip a new helm.

Blowgun: your blowgun loses the loading property and your normal ammunition now does 1d4 poison damage with a 10 + (your proficiency) DC CON save to be poisoned.

Boomerang: your boomerang now comes back when you hit as well as when you miss and has a chance to stun your opponents (10 + your proficiency DC DEX save).

Club: you may now use a reaction to hit back projectiles with a range of 15-30 ft for 1d4 (whatever the projectiles' damage type was).

Crossbows: your crossbows now lose the loading property and gain the piercing property (your bolts can pierce through 1 wall/enemy/obstacle).

Dagger: your dagger gains the precise striking property making it ignore resistances and immunities.

Dart: your dart gains the bullseye property making its critical hits do quadruple damage.

Double-Bladed Scimitar: the special property now allows you to do 2 bonus attacks instead of 1.

Flail: your flail may not be parried now.

Glaive: your glaive now does 2d8 damage and loses the heavy property.

Greataxe: your greataxe now loses the heavy property and gains the sweeping edge property (your attack now ALWAYS attacks 3 squares, 2 to the sides of the creature you're attacking).

Greatclub: your greatclub now has the versatile property (1d8 one-handed and 1d10 two-handed).

Greatsword: your greatsword loses the heavy property and gains the versatile property (1d10 one-handed and 2d6 two-handed)

Halberd: your halberd loses the heavy property and does double damage to mounted enemies.

Handaxe: your handaxe gains the shield splitter property (if the target has a shield and blocks your attack the target's shield is split and becomes unusable).

Javelin: your javelin gains the piercing property and gains +2 attack.

Lance: your lance loses its special property and you effectively has the charger feat when you're mounted. 

Light Hammer: your light hammer gains the returner property (it comes back after you throw it).

Longbow: your longbow loses its heavy property and gains the bullseye property making its critical hits do quadruple damage.

Longsword: your longsword may now be used two-handed while using a shield and you still reap the benefits of the shield.

Mace: when you roll a 6 for your damage roll the target must make a 15 + (your proficiency) DC CON save or be knocked unconscious.

Maul: your maul loses its heavy property and gains the stumble property making anything you successfully hit not able to move until the end of your next turn.

Morningstar: your morningstar gains the pushback property making anything you successfully hit get pushed back 5 ft.

Net: your net's special ability is completely revamped "A huge or smaller creature hit by a net is restrained until it is freed. A net has no effect on creatures that are formless, or creatures that are gargantuan or larger. A creature can use its action to make a DC 10 + (your proficiency) Strength check, freeing itself or another creature within its reach on a success. Dealing 20 slashing damage to the net (AC 10 + your proficiency) also frees the creature dealing the same damage to the creature, ending the effect and destroying the net." and is now considered a melee weapon.

 Pike: your pike loses the heavy property and gains a throwing range of 10/40.

Quarterstaff: your quarterstaff gains the thrower property (anything you successfully hit you can have a grapple check against them to throw them into any unoccupied space within 10 ft of you).

Rapier: your rapier may not be blocked by a shield.

Scimitar: your scimitar acts as a +1 scimitar.

Shortbow: if you roll a 6 for your damage a limb of your target is pinned by your arrow with a 10 + (your proficiency) DC STR save to free themselves per arrow.

Shortsword: your short sword acts as a +1 shortsword.

Sickle: your sickle gains the reaper property (if you could kill an enemy with max damage you may instantly kill them if you hit regardless of your damage roll).

Sling: your sling does double damage to creatures of large size and bigger.

Spear: your spear now has the reach property.

Trident: if you roll a 6 for a thrown tridents damage the target is pinned and must roll a 15 + (your proficiency) DC STR save to pull the trident out and your trident acts as a +1 trident in rain or underwater.

War pick: your war pick does double damage to constructs.

Warhammer: your warhammer gains the stumble property making anything you successfully hit not able to move until the end of your next turn.

Whip: you may now use your whip to grapple enemies you hit and swing across gaps.

Yklwa: your yklwa now has the piercing property and pinning property (if you roll an 8 for thrown damage your target is pinned and must make a 10 + (your proficiency) STR save to remove the yklwa).