The parks are indeed, very crowded on Thanksgiving and the day after. We departed that Friday so I can't provide you with info beyond that.
It was an early opening at MK that Thanksgiving in 2003 so we high-tailed it to the park and then left at 11 a.m. We then went to AK where the crowds were very manageable. The day after we went to Epcot for the morning. Left for lunch at WL's WC for lunch, meeting my mom.
When she left, we thought, what the heck, let's try the MK, only a boat ride away, for a last attempt. OH MY GOODNESS! It was crowded beyond my wildest dreams. We just ended up winding our way around the park and leaving to get back to the WL for our airport pick-up.
Hope it helps! Think early start on those weekend days and be ready for lots of easy on and off when the holiday crowds depart!
--penny