You can equip higher level stuff, it's based off of equipment expertise, not level.  Higher level stuff costs more expertise, and when you run out you can't equip any more higher level stuff. 

I don't know that the damage should be the same.  What are you using? 

It's cuz at lower levels your unarmed damage is higher probably.  At higher levels, the quality of weapons will scale up and it'll be wiser to actually use a weapon.

Well yeah, your unarmed damage is on pair with a green item right now. 

Your original question is "I don't get extra damage from equipping these handwraps," and then you just said "my damage is a lot higher with these on though..."  So........ ?

I don't think anybody says that.  Having good weapons is always better than unarmed, but unarmed is better if you have crappy weapons that aren't uncommon or rare.