The 80 lbs. thing in laws is a throwback to when many/most boosters used to have that as their top weight rating, and nothing higher was available, as I recall.
The belt is actually designed to work properly with a 40-50 lb. child in a booster (lock in case of a crash.) There is no minimum on weight it's designed to hold, though a 20 lb. kid in a booster might not trigger the locking mechanism, of course that's one reason boosters have minimum weights. Seatbelts working properly has to do with fit and positioning (the
Five Step Test, as Wendy mentioned) and while many kids will pass the test between 4'9" and 4'11", there are kids who do before that (as early as 4'7" in some cars for some kids) or after (as late as 5'1") and then there are the seating positions that no one passes in (there are occasionally even recalls for horrible seatbelt geometry in some cars... And many women find because of our different shape, with, you know, the bustage, even at 5'3"-5'7" there will be cars where we don't pass the shoulder belt portion of the test.)