I have the same issue more with pelvis soreness and it's an all day thing. I recently read and talked to a few of my girlfriends that are moms that it happens around now because the baby is starting to turn head down. And you are beginning to stretch down there for delievery. Unfortunately I have not found a good way to sleep.
That's most likely what's causing it. I don't have pelvic soreness, but my belly does hurt if it's not very well supported at night. I actually place a really thin pillow all the way under my bump in addition to cuddling the snoogle. It really helps.
I wonder if it would help you to wear a maternity support belt during the day. Maybe the reason you are so achy at night is bc of a lack of support during the day.