Pre is fine to call when BB is fish. Nothing I do too often but it's exactly the hand strength for doing it when you have a BB behind that calls a lot.
You can only fold the turn if you think he has just zero bluffs. But I dont think that's the case…
Quote from chitz: “if SB didnt cold call the 3b then JJ is an easy 4b and call vs jam, it gets much closer vs those tight NL10 3b and 5b ranges.
You 4b/call JJ MP vs BU? That's too loose for sure.
Anyway, I like 4b if these guys are not too tight.
I mean the hand is played fine for sure. But turn is just thinner than you expected it to be, because it's MPvBB (I'd almost always 2barrel BUvBB).
Regarding flop: Axx boards with two low cards very rarely have a cbet freq >60%.
You should bet the turn bigger. 1/2 is too small. Actually it's very bad.
Just bet the river. What are you afraid of? He has very few better hands.
Edit: Okay I take that back, big river bet is too thin. But I wouldnt check, small bet looks good.