It's a 762. And yes, certain days of the week are more prone to 100% full loads than others namely Thursdays, Sundays, and sometimes Fridays. Usually however, there is some room for last-minute bookings.
Surprisingly, non-revs aren't always as lucky on those flights. (There tends to be tons of FA commuters using that flight to get home or work.) The combination of revs and non-revs on red-eyes make for full loads. Paying pax get first priority on getting on, obviously.