2nd hand at table, effective stacks $100.

1. Folds to me on the SB, I raise to $4 with [Kc]. BB calls.
2. Flop [7h][3d], pot $8. I lead $7 and BB calls.
3. Turn , I lead pot $22. I lead $16 and BB calls.
3. River , pot $54. I check, BB bets $40, hero?

Another option would be to lead $30 I think, but I'm not sure how much value the 3rd barrel has against a J (though this is a blind war).

That depends on whether you think the opponent is aggro or not. If it's the 2nd hand you've ever played with him, then you have no reads ... in that case I think most players tend toward being more calling stations than overly aggro, so I would slightly prefer a value bet on the end (fearing a check behind from a hand that would have called a bet).

Bet/fold the river here...checking is VERY bad.