Check-folding flop is horrible but check-calling is not unreasonable. FD is extremely unlikely and if he's on a lower pair he has very few outs. There are many ways a check can extract a little extra from the villain:

- it might induce a bluff,
- villain might call more lightly on later streets because he doesn't believe we have an A,
- villain might catch something on later streets that he thinks he can call with.

The main downsides of checking are:

- the board may turn too scary for the villain (low PP's are a big part of his range),
- having to play later streets oop with little information on villain.