I think the bottom of the ring is always thinner than the rest of it, mine is. I got my ring resized 3 times before finding the right size. Mine still spins as well, but the jeweler told me all rings do that unless it's way too small and can't move at all in which case you'd have a hard time getting it on and off. It might just be top heavy. They have something called ring sizer beads that they can put on there that will allow you to get the ring over your knuckle, but it should stop it from spinning as much. I would do some research on it first though.
If you have a large knuckle and skinny fingers, your ring might just spin. Taking metal off the sides of your ring is not going to do anything.
You can get "sizing beads" added. Those are like little nubs on the inside of the ring that will help create a tighter fit without decreasing the inner circumference, therefore still allowing it to fit over your knuckle. I would reach out to a jeweler and let them know what you are experiencing and see what they recommend. Don't hesitate to bring your ring to a few different shops to get different opinions.
If you are worried about how thin the bottomed portion is a jeweler can add a half shank which will build up the bottom. I see what you are saying about the sides, but maybe with the half shank added it might balance out. Spinning happens, like others have said getting the nubs inside could help.