Your hand is not strong enough for a checkraise and villain has no real bluffs, so betting will be better than check (call/raise).

What sizing?

Your sizing is ok, your opponent has a lot of Ax that can call a small, but not a big bet.

But I would bet larger against a good reg with my whole betting range, you have a polarized range here and you still want to have fold equity for your bluffs.

I would just shove being that high in a range OTR.

We're only behind KT/TT/44. Not a lot of combos, depending at villain's preflop choices its propably between 7 and 5 combos. If you cant shove river against that with QJ, it usually means that he's overfolding somewhere like crazy.

I agree with the combos you give him. Perhaps also add in some AK, people do fail to 4bet this sometimes.

But the next question is what combos does he call with? I can't think of that many particularly with our blockers.

I just ran a sim in piosolver for this hand. The problem is that I need to make a lot of assumptions about ranges etc. But interestingly it seems to think that checking and betting with the exact combo I have is okay (with a slight preference for checking). It actually has more bets with other QJs combos.

I think we can give Villain a somewhat wide Flatting range mainly because SB will generally have a strong linear 3B range in this spot, and if they had a hand like QQ+AKs, they are most likely 4Betting a high % of the time. Even if a rough estimate of 11% flatting range is somewhat reasonable assumption it think.

The idea im thinking of (which u may want to look at in PIO) is what if we generate a Overbetting strategy on the Turn. Even if the villain flats a hand like AA in this spot, and we over bet..they are going to feel pretty sick. Im not saying its a good idea, or the best one, heck it may be the worst idea ever and im open to hear why, It just may be something to look at. If we get called OTT after we overbet we can assume we are beat, could possibly Jam River if we hit are straight as it's most likely our only option.. Check/folding seems pretty weak with that line, and villain will have all AK and TT combos in their range as well.