(22s) AA hitting a set on the flop

this just happened to me three times today but so what happens is...

i look down at AA UTG, level 1-3 with everyone still on the table, so i decide to check (probably mistake number 1) hoping for a raise so i can reraise.

everyone folds, blinds call, flop is Axx
blinds both check to me, nothing too threatening out there, maybe a gutshot but i'm not worried.

should i bet? out of the three times i bet twice (3/4 to the pot) and it was folded to me, and then one time i checked, the turn was a 2nd space where the bb raised, i reraised and he called, and last card was another spade.

i was hitting myself over the head with this telling myself slowplay isn't that optimal with a full table early in the tourny, but anyone have any thoughts on how to play this?