I put a 2.1 tire on rim that usually uses 2.0. When I pedal the rim bends on the sides
Judging by your last photo you have somehow unscrewed your cup&amp;cone bearings at least partly, making your bearings extremely loose.
Bearing play should be carefully adjusted. You usually need special, thin wrenches to adjust bearing play.
You might have lost some bearing balls in the meantime. While you are at it you should re-grease them. Probably best to visit a bike shop.