I would start by betting bigger on the flop. I think the cold callers flop calling range isn't going to change much if we bet 50% and there are a lot of hands he will call with that we are doing really well against. I check turn also and I think it's fine to overcall. I reckon our hand is going to have enough equity against their ranges and I don't expect them to be so nutted because of the sizing. I would expect population to just bet bigger with sets on this turn as it's now a pretty dynamic board.
I like your line, also betsizing on flop I like, not like we need much protection with our range here and we want to keep in pocket pairs and 7x type hands, no problem to keep in gutshot hands from bigblind either, this is actually a very good sizing giving board and ranges that also gives us still leverage on future streets. So dont agree with above comments.
Like your turn check as well and given action im calling turn most likely giving up to further river action. Definitely not a super comfortable spot anymore however bb can still have a bunch of Tx, 7x+fd type hands plus im expecting him to donklead a hand like T8 some plus expect him to checkraise sets alot too on turn as well as two pair sometimes. So cutoffs range is actually stronger to me than bigblinds. Simply because its harder to find worse hands than ours in his valuebetting range. But his sizing is super small here, to me such a sizing in a multi way pot with an aalready bloated pot means he is either super strong like set or better or he is blockbetting to buy himself a cheap river hoping it gets checked to him when he bets here.
Now I dont even think on this board now he would bet sets small like this given action and its very hard for him to have J9s given we have JJ and given we raised UTG. So thinking about this further, not even his bet is very concerning here. The problem is that we dont really get value from worse by raising, but cutoff and bb probably have decent amount of equity combined vs our hand.
Given all that I think its a pretty easy call on turn and I dont think there is any better alternative here. Expecting blank rivers to get checked through alot actually
what we could potentially do as alternative to call turn check river is donkleading river small on blanks ourselves, that should actually be even more ev than checking given what i said above. Highly doubt cutoff is going to bluffraise much. Bit more potential for the bigblind for that, as well as a bit more potential for him to have a straight or two pair but the frequencies of that i still see as very low for him. But def would consider this line too here, its an exploitative play though, as we dont really want to just checkcall alot of sets on turn given board and action. Its just that by now both their ranges actually seem pretty weak to me, so that on blank runouts im expecting us to have the best hand alot