I'm probably folding the turn when they raise, we have no FE when they make it that size and I expect draws (very few) to raise the flop if they were planning on getting it in. They do have 77/33/22/99 and 23/79 given they limped.
I think in spots like this it comes down to what you think they think a value range is here and what percent of their value range do you beat. It is unlikely they have enough combos of hands like JJ TT 88 or semi-bluffs like 7xhh / A4hh etc that they play this way. There are players I play with who will do this with a lot more combos of hands than 22 33 77, but there are also others where they literally only have 22 33 77 99.