I'm not an advocate of stats in general when analyzing these general situations.  Sorry if it sounds harsh, but the fact that you advocate flatting a 3-bet, is tilting me. With three handed dynamics, JX trips is essentially the nuts in any situation. And the cons of villain outdrawing you on turn/river street far outways the fact that villain might have you beat with better JX+. and AJ is likely 3-betting preflop. 4-bet jamming is definetly the +EV play here. And maybe this villain flatted KK preflop to trap, and was jamming on any board. theres no way i would flat JX on flop

1)　I'm beating all VIllains PP hand range other than 44

2) Im beating all 2J-TJ hand range, which is likely BB flatting range

3) Villain is likely 3-betting AJ+, JKs+, thus further cutting into number of value combos thats beating our JQ hand range

4) Whats the purpose of flatting the 3-bet on flop, if we're not going to fold the hand anyways on a later street. the only thing we accomplish, is allow villain to catch up either by hitting his 2-outer, or 8+ outs for Flush.

5) by jamming , you also set-up a dynamic on Paired board textures, and you can also gain information on what villain is min 3-betting with on paired board textures, thus exploiting him in the future.

Hey TheLove, you don't have to say sorry,  I welcome any discussion.   My thought is that , this type of player won't 3bet AJ that often, so he could have AJ, KJ in his preflop flatting range.  But he don't have AA/KK/QQ in his  preflop flatting range.  With pocket pairs lower thant TT, I doubt he would lead/3bet/call on the flop.   

I don't consider protecting my hand that much in this situation.  Although this is a two-tone board, I doubt this type of player would raise his FD on a paired board.  From my experience, this type of loose passive player mostly call with draws, occasionally they lead, they would just call your raise instead of 3betting.