OP had concern about:

(I know this route is subject to weight restrictions, so I'm curious just how many empty seats they'll fly without filling.)

According to TravelNet this route is not listed as weight/balance op critical "BUT" if weather parameters strong headwinds westbound
occur it could be with a full passenger load - eastbound flights usually are no problem with tailwinds. When you list for these flights
before TravelNet directs you to the available flights a window will appear advising of the restrictions.
Hope you fly the front cabin - Good Luck !