I would bet the pot
The pot is big already related to the blinds and the stacks
You still have a massive draw (counted 28 outs for nut high or/and nut low) and it's mot likeky that nobody has a set of Jacks (he would have probably bet the pot on this board to try to protect his hand), I can't see anydody having a set of

(what would he have called the flop with ?)
By betting, you can get heads-up which may help you win high even if you miss (like you're heads up with a A245 hand : any Jack or 9 wins high)
If you're called in more than 1 place, you need to improve but your pot equity is huge
By checking, you let them the chance to beat you with a mediocre hand (say somebody has A257 and hits a 5 on river or TJQK and hits an offsuit 9,J Q K) and you don't want that
Just my opinion