[Doc]

lots of points there!

J7s is a 50% hand - in that it wins heads up against a random hand 50% of the time. However heads up play in reality is all about aggression and stealing blinds. With a massive chip lead, you need to keep the pressure on. I wouldn't call an all-in from the other player pre-flop yet, but unless you have strong reason to suspect he is trapping, then T7s is exactly the sort of hand to get aggressive with when he has shown weakness. You need to ask what is a good flop for you? It will be hard to be confident, so try to take it down now would be my strategy.

When the chip lead, the blinds and the fact that he will have to call for all his chips are considered, then T7s is +EV here if you move all-in pre-flop, no matter what he'd call with. Moving all-in mightn't be the optimal play, but it is a good play.

The play post flop is way too passive IMO, but I illustrated the call mathematics just to show that it is far from an outlandish play to call his all-in. My (and I suspect most players) gut-instinct would be to fold, but is there really a 13% chance he has a Jack or a 7? He has played it very poorly if so.