assumption:

villain flats the following range with AK and QQ being 3bet 25% of the time

QQ-22,AKo-AJo,KQo,AKs-ATs,KQs-KJs,QJs,JTs (121.6 combos with hero having the blockers)
this range has TP+ 25.9% of the time.
on the board of AcJc3d it has TP+ 31.1%. What has to be taken into consideration that villain has only KQs as a flushdraw in his range

i assume hero is opening is about the following range
AA-22,AKo-A9o,KQo-KJo,QJo,JTo,T9o,AKs-A2s,KQs-K8s,QJs-Q9s,JTs-J9s,T9s-T8s,98s-97s,87s-86s,76s-75s,65s,54s (326combos)

if we look at a random flop this ranges has TP+ 25.5% of the time and on AcJc3d has TP+ 31.5% of the time but has far more often (14.9%) middle pair.

lets  look if we should Cbet with our entire range we can look at pokerstove. If we compare the two ranges on the board we are actually a 45:55 dog on the board
So a Cbet here is not appropriate with our entire range.

Therefore, from heros perspective we should be well balanced here with bet/x, c/c, c/f, c/r. I wont analyze every action in detail.

in a vaccuum i would say check/calling KJo here is the best line. but lets look at this in more detail

lets look at villains range and use Andrew Brokos hand reading system:

villain has:

Monsters: 33,JJ,AJ,AK,AQ

Marginal: PP,ATs,KJs,QJs,JTs

Draws/air:KQo

by checking hero indicates that he has a hand which has some sort of showdown value. Most likely hero would bet all his FDs, TP+ hands on  this board.

Therefore i assume villain if decent hand reader bets the following hands for value

33,JJ,Ax,QQ,KQcc

he checks back most of the SDV hands (PP,Jx)

so his betting range is

JJ(1), 33(1), AK(6.3), AQ(12), AJ(6), ATs(3), KQ(12), QQ(4.2) against this range we are 26:74 dog. to actually make a BE check/call we need 35% equity.

so which turn cards are good for our range?

i would say K and J should give us more equity.

lets see how differen cards change the equity of ranges vs hand:

Kh: 48.5:51:5
Kc: 51:49
Kd: 49:51

Jd: 20:80
Js  18:82

looking at this the flop vs a verytight/nitty player is a  a check-fold. also we only have 5cards in the deck that can help our equity to cathc up

Turn:
on the turn we get probably the best card in the deck for our hand. our equity goes up (almost doubles) its now 49:51 dog. Further we migth have more FDs in our range and the flush may slow the villain down from raising and stacking of with his sets
therefore we can bet out here. also our bet seems to be hihgly profitable as we have 48% equity but need only 38% to make a BE bet. Further, betting here may also often lead to a check back river and save us some money

without going into further analysis it should be clear that if we bet the turn we have to fold to a raise with the villain having such a tight range.

i also think it sets up for a c/f on most rivers if villain just calls our bet.

in summary might thoughts:

-preflop: seems fine
-flop: check/fold as we are getting not nearly enought odds.
-turn: bet is ok. with the added equity we can almost bet marginally less than pot size and we are still BE betting. So i guess bet should be slightly higher. the problem here is do we
know that villain has an elastic calling range or does he have a static one. If he has a static one then i def want to bet >2/3 pot

cheers