You're behind preflop and way behind on flop. Only pot behind after you call PF. You can't go flop shopping here and you don't have postflop FE. Fold PF, fold on flop.

Preflop: AA-KK/AK, maybe QQ/JJ

Villain's postflop check doesnt narrow his range. He either slowplays AA/AK, or chose c/c line with JJ-KK - he isnt folding it with pot behind.

Check behind, this hand becomes an auto stack-off if a ten hits on the turn..
FYP