I am trying to figure out if you play a tiny character, does your weapon damage change ? Would a dagger still do d4 damage, or something else ??

As far as I know, there are no official provisions that deal with characters smaller than "Small", so it's entirely DM / homebrew territory.

Standard equipment does have some handling for Small characters, namely with the Heavy weapon property. A halfling using a dagger isn't using a smaller dagger, so it still does d4, but at the same time a halfling has trouble wielding a greatsword.

So, if you want to play a Sprite or something, I imagine your DM would have to classify weapons that would be "heavy" for you, and "too heavy" for you. And perhaps make a couple new weapon types for your size, with appropriate damage ranges, like a needle or a razor. >.>

Or perhaps make tiny-sized equivalents and adjust their damage range (and weight) appropriately.

I mean, look at the aforementioned Sprite. It has "Longsword" and a "Shortbow" in its attack actions, and they do 1 damage on hit.

There are no official 5e rules for tiny PCs, I'm afraid you'll have to dip your toes into homebrew.

The best I can give is the mods created for a Reduce Person on an already Small Person

Reduce. The target's size is halved in all dimensions, and its weight is reduced to one-eighth of normal. This reduction decreases its size by one category--from Medium to Small, for example. Until the spell ends, the target also has disadvantage on Strength checks and Strength saving throws. The target's weapons also shrink to match its new size. While these weapons are reduced, the target's attacks with them deal 1d4 less damage (this can't reduce the damage below 1).

I think most tiny creatures have a damage output of 1, that's how I would run it anyways.