Hello. I am running an adventure, based on prewritten material ( Tyranny of dragons)  The wizard loves playing giantess characters, and I want to make a balanced ability for them so they can go up some size catagories. 

I know it will be a limited use feature, returning to their base size so they can still get into places. 

I also want the max to increase as the story moves along. 

What I don't know is the best way for the stats or any damage to change while still primarily being a caster as not to our perform the martials or trivialize combat or other encounters.

Why not just encourage them to take enlarge/reduce as a spell, and use it when appropriate? If you want to be really nice, you could give them a homebrew item that lets them cast it on themselves 1 or 2 times a day.

Being bigger really wouldn’t do much for a wizard. Besides the spell, there’s the rune knight ability that lets you grow one size category. In both cases, it gives you some bonuses to str checks and saves, and a little extra melee damage. Neither of those is likely to matter much to a wizard — it won’t change their spells at all, and unless someone is trying to grapple them, the str checks won’t come up often. So their dagger attack will do 2d4 instead of 1d4, so they’re still better off casting fire bolt.

And I don’t know if I’d let them just switch between sizes too easily. D&D is about making trade offs. Getting one thing means you aren’t getting something else. If they’re going to be able to get big, there should be a downside, so they need to think about when best to use the ability.

I am using that as their ability. 

The only complication is going more giant size.

If they want to be closer to the Huge/gargantuan size catagories. Though I may have something.

Just keep things simple and let her stack the Enlarge/Reduce spell.

There's the Goliath race, which is distantly related to giants, and you might also want to take a look at the Graviturgy wizard subclass. The Adjust Density subclass feature acts a lot like the enlarge-reduce spell, but has a size restriction, which changes at level 10. If you don't want to use the subclass you might at least use it for some ideas.

At the risk of being a bit crass, sometimes people just need to accept that the D&D system doesn't offer a good way to accommodate a particular character image, particularly when it come to large-scale physical attributes or other more fantastical elements. This isn't completely unworkable, but if you let them get up to Huge I believe you'd technically be quadrupling their ability to lift, push, and pull objects, based on how Size interacts with the Strength score (capacity is based on STR and doubled for every Size above Medium). A magic item that lets the user cast Enlarge/Reduce 2 or 3 times a day is somewhere between an Uncommon and Rare quality item per the DMG guidelines, probably closer to Uncommon if you leave it at self and Enlarge only. Would have to weigh if you want to keep or drop the concentration requirement.

Quote from pocketmouse >>

There's the Goliath race, which is distantly related to giants, and you might also want to take a look at the Graviturgy wizard subclass. The Adjust Density subclass feature acts a lot like the enlarge-reduce spell, but has a size restriction, which changes at level 10. If you don't want to use the subclass you might at least use it for some ideas.

 There is a play test version of the Goliath in the 1D&D Unearthed Arcana for the Cleric which allows you to increase your size to Large. It’s only once per long rest, lasts 10 min, gives advantage on Strength checks and +10 ft speed. You probably could stack Enlarge/Reduce on top of that. 

https://www.dndbeyond.com/magic-items/5522-potion-of-giant-size

This item comes from the Storm King's Thunder adventure. It makes the drinker huge size for 24hrs and gives mechanical changes for their new size.

Note that the above potion is of legendary rarity and in no way should those mechanics be applied to something you could use every day.

"Large isn't big enough" doesn't really sit well with me as a player attitude. Why not? Large is still very big, just lean into it and you should be fine. Do they want a specific mechanical benefit for being huge?

I mean I'd like to progressively turn into an ancient red dragon as I level up, but you just can't always have everything you want. So you look at what you can do and you go with that, supplementing with roleplay and flavor. Bending the rules to accommodate one player's fantasy can risk drawing the resentment of the other players who are literally playing in the shadow of your giantess wizard.

Thank you all for the ideas. I found something that works with the one DnD exhaustion mechanics and the Fizbans feats for a base large( borderline huge caster, with the dragon theme and can still return to size but it costs something.

There's always the Polymorph spell... You could homebrew allowing it create non-beasts.