Should I have folded rather than called/jammed turn

Hi Nick,

I probably played this hand poorly in a number of ways but I felt it made sense based-on my familiarity with the opponents at this point.

Notes: I began limping my entire range from early position due to the table dynamics which were that there was an opening raise virtually every single hand (the amount was almost always $20-25 no matter how many limpers before the open came) with virtually no 3-betting of the open and two or three+ callers of that single open (and I had other player specific reads as well). My plan after limping was to call if the open came from early position or if the odds were compelling due to number of limpers (I would do this with 22-JJ and AJs/AQs), raise AK+/QQ+ if the raise came from early position, and raise if the open came from middle/late position (I would do this with all of my range). I felt that I could get away with this as my opponents did not seem aware enough to adjust appropriately.

I had a hard time putting cutoff on non-two-pair 3x hands (because he called pre-flop open and $75 flop bet with just bottom pair) or on AA or JJ (because he would likely 3-bet as, even though 3-betting was rare at table, these hands likely do it). I did think he could have A3s (maybe even 1/2 of his A3o) and, of course, he could have AJ or the last combo of 33. However, given that the made combos that beat me that he might play this way were fairly small in number and given that he was very capable of playing this way with non-two-pair Ax hands as well as flush draws, I thought I could get value or possibly fold-out the 3x hands where the x was low with my jam.

Anyway, please evaluate this hand for me throughout (although, I really want to know if I should have just dumped my hand after the turn raise).

Thanks!