HGIYLHE Question on Hand 4

For those who have this book, perhaps you could comment on the river play in Hand 4. If it is recommended to check/call here, why would it not be better to bet/fold instead? Seems like we can be pretty sure the villain will bet if we check, and that we are likely beat...but either way it costs us 1 bet.

However, it seems to me like villain might fold even two pair (assuming he has AA88 with a better kicker) if we bet. We c/r on the flop and 3-bet the turn...he could be very well convinced we have the 8, no?

[Sorry if this post belongs in the Books and Pubs forum, but I figured if I have questions about playing the actual hands, it would be best to post it here.]