+Character Size

So, does increase character size give you bigger AoE for things like Sweep or just general weapon reach?

I doubt it, i think it's just for showoff, but we will see what other people have to say.

It really depends on their engine. I cannot be sure without words from GGG. Normally, non-melee effects originate from the center of the character so it wont have any effect (Frost Nova, Shock Nova, Discharge...). Melee attacks however, usually calculated from edge to edge of the character (for visual purpose) so you will get a better reach with a bigger character size and also easier to get hit from meelee attack. Character hitbox is a different issues, but still relevent for this amulet. From the look of their unique item dev diary, you should get such kind of drawback for using it.

I just talked to Chris about this. The increase in character size is entirely cosmetic. You don't get a longer reach on your melee attacks. Also your hitbox remains the normal size so you won't get hit more by Firestorm or similar multiple projectile skills.