We have been the last 3 years during the week of the 4th and YES the 4th @ MK is unbelievable! Wouldn't recomend it on the day of the 4th, we always do EPCOT and AK seems to be alot less crowded. The week leading up to it can be little hectic water parks get pretty crowded as well.
But hey your @ DISNEY!:sohappy:
Also seems to rain bout everyday that time of year usually in the afternoon 2ish or so but cools it down a little but gets humid after that so keep poncho's handy. We will be there @ the same time 6/28-7/5 @ Boardwalk. If your staying on property just plan a few breaks, afternoon swim nap whatever during the peak sun time, and ALWAYS lots of bottled water (tap water is awfull) we always bring a case or 2 and put it in the little freezer in the room fridge that way we have cold water all day, fits nice in a pack (yes I wear a pack but only while in the world, my DW's idea, love ya honey ) and helps keep ya cooled down works GREAT!