Stars $400nl JJ in a 3b pot oop

[Trivial]

you can check call the turn and decide on river if you suspect a float (i'd very rarely fold the turn) since his value betting range is very small here. i've been guilty of check calling down with as bad as pocket deuces in these spots against float-happy types but in general i think most players won't bet the river with air once you call the turn, since your intent is clear.