What to wear underneath sleeveless tops and dresses.

I’m looking for something to wear underneath. Now that I’ve successfully lost weight, I’d like to keep wearing sleeveless tops and dresses. But since I now have what’s called “flabby arms,” I need your help.
The sleeves should go almost to the elbow—they can be shorter or longer; I can always adjust them. An underbust elastic band or cuffs would be good.
The fabric should be very thin and stretchy.
Is there such a thing?