This flop is a must bet -- we're usually ahead here and I think what folds is what may beat us on another street (e.g. AK) and what stays is what we beat (1010 and down)

Checking JJ on a flop like that, you might as well open-fold IMO ;p

$45 on flop, 2/3 pot turn

as played on river you have to c/c, I don't see how we can lead there
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mini, it would be much much worse to check the flop if it's HU, we're a ahead a lot more in that case and our hand has a hard time holding till river. Multiway, I'd say we have at least a 50% chance we're ahead so we have to bet to hopefully take it down there.