Overpair and OESD: What do you do?

[SuitedSixes]

I have had this exact situation come up twice in the last month, once live and once virtual(?). After the flop, I end up HU with a similar sized stack. I have JJ and the board is 89T. In both cases I was on the button.

Live, it was the beginning of the 4th round, Blinds (200-400), the (non)action folds to me and I raise to 1200, I am only called by the BB, we both have about 4,800 left after the PF raising (Pot, 2600).

Online, it was it was early (1st or 2nd round). I had limped in on the button, and the BB made a min-raise, I was the only caller.

In each case, I made a pot-sized bet and was check/raised all-in. What do you do?