Forgot to mention - I'm assuming our opponent is at least semi-rational, capable of reading pot odds
and not a complete donk. Given no reads on the table, I have to assume the bad guy is an "average" player.
look at the betting habits here, and our opponent only has one of three hands: AJ, 44 or the flush. All 3 could limp the flop, and all 3 will call the flop bet Hero makes.
With the size of the bet on the turn, a FD should have folded - not impossible to call on the implied odds, but most people will fold it here.
44 is still calling (he's got a set, so he'll let you bet for him). AJ might call (wondering what your kicker is), might fold.
The betting so far points towards hero having an A - it is really hard to read that a new player has a set.
River J. 44 still has his set, no pair on the board, and Hero's bets make it unlikely hero has a flush - He has to put hero on an A, so he will raise to try and get some more chips out of Hero. AJ now has top 2 pair, and will raise because he knows he now beats any other A. The bad-odds flush also raises.
So we beat two out of three probable raising hands - and the flush is the least likely hand of the three. that's an easy call for me.