QJ is a very small part of his range and he would be jamming the river with it a decent percentage of the time. I'd be more worried about 53 given the reads you have on villain.

In first glance this looks like a good value-bet to me, but I think that doing some analysis on villain's river distribution would help us determine the right play with greater certainty.

53 seemed unlikely to me when he called for a second time but I think this was a flaw in my thinking (I was focused on what backdoors/2pairs the turn brought in that could enable him to call twice, sort of dismissing 53 as "he wouldn't call twice with just that there")

If he has T2xx, A4xx and A2xx hands for us to valuebet against on the river then it's reasonable to assume he also has T53x, A53x, 532x, 543x also as well as the KTxx, ATxx, QJTx combos. The more I think about it the more it feels like a c/back, even if we are good here most of the time he still has to be calling off with 2pair etc for a shove to be good. If he gets away from these sometimes then the value gained by jamming goes way down. I suppose as a fairly close spot, you can't really go too wrong either way with it.

I like checking back here. I think you hit the nail on the head when you say villain has to be ck/calling 2 pair hands here, which I doubt most villains will be doing. Also silly question for you- are we completely ruling out AAxx from villain's range? It seems like a really weird/bad way to be playing Aces and villain would probably be limp/3betting and not limp/calling with AAxx. Just a random thought

Is this a std flop raise? Even though he made it that small, I'd be enticed to just flat. The board is super dry so I wouldn't be concerned that much about giving the 3rd player odds and we can have a better grasp of where we are OTT.
And I wouldn't know what to do on most turns if our raise gets called by the leader or even both and the turn is a brick.

I play a lot at this stake, though I am a spewy BE/small winner :).
In my experience even fishes dont stack that easily without near nuts or second nuts on river, on the other hand they will call with shitty gutshot+draws till river. Which means:
FLOP: I skip the flop raise part, after some thinking I kinda like it, though not sure how good/bad it is. (On one hand there are not many strong hands on a board like this so you protect/on the other hand you wont improve many times)
After villain calls, I put him on weak two pairs, pair+straight draws, TP+overs, overpairs+some random weaker hands. I think top two and sets would jam, but if not on flop they will on turn.
TURN: Now you got the nuts, but a fd came down. I definitely dont like your betsize, as I said fishes go to river with even the weakest draws, I would bet 9+. After call his range wont change much, possibly folds some weak two pairs, maybe some pair+gs.
RIVER: Big guessing game, in my experience the number of combinations that calls and we beat are smaller than the number of combinations that calls and beat us, so I would check.

I like the flop raise as I expect to be ahead of the donk bettors range even when called due to his sizing. Flatting such a small lead turns our hand a bit face up imo, if the other guy calls behind then I'm going to give it reasonable credit and won't be putting much money in unimproved. On river I guess we would need to do some
calculations on required calling ranges. I get the feeling that the decision is actually very close and is something we can't be very accurate with as it's impossible to know what range a random fish gets to the river with (does he smooth call bottom set on the flop or go with it for example?). We also don't know if he checks the river nuts, or if he will call with 2 pair. I suspect that even if we are good here most of the time, there just aren't enough combos of worse that call and checking back is the better option.