The weatherstripping is most likely very old and not as soft/supple as it should be. You can replace the weatherstrip that is there with some new stuff and if that doesn't fix the sunlight/draft coming through you will have to adjust the catch on the door to hold it closed tighter against the seal.

Jason
M80 v2
VP160 v3
QS8 v2
PB13 Ultra
Denon 3808
Samsung 85" Q70