[DeeJ]

He knows that with the K on the board, if you've both got AK he's tied. If you've got AK or AQ or AJ he's ahead with 77 or 99. As far as he can tell there's no real draw on the flop, and only a thin one on the turn with your hand range. I guess he's on AK here more than anything else. But he could have QJ and want the extra bet, or maybe 3 if you raise the river, being unwilling to raise the turn and push you off a totally missed hand like AQ.

He could have a random bluff holding like K9 or T7 though if he's tricky. I don't think you can play this any differently without being totally weak; he could have TT or JJ after all and be a donk.