Villain is 40/15 after 50 hands, AFq is 30%

First of all, should I have 3bet this one? my double pair makes it a better multiw3ay hand, but my flush and straightdraws would prefer HU. The somehwat good thing is that we have 38% against AA**, so if he 4bet we can get it in/dont have to fold.

On the flop I thought it looked a lot like scared AA, so I decided to bet with the intention of barreling and winning the turn quite often. When he calls again I was kind of puzzled. Maybe he has something else or maybe doesnt like folding AA? That leads to me not knowing if I should bet the river. He might have played it this way with a straight draw that hit the turn and would fold now.