It's not unstaffed (as a station), the ticket office is, but there are still staff available until the station closes
At a recent meeting I attended, an SWR manager was tackled about this state of affairs (the toilets), and apparently the best suggestion is to simply use the ones on the train. Given the state of the average SWR/GWR onboard toilet, and the fact they are often out of order as well, people in the meeting weren't convinced.
Of course, what amazes/saddens me is how people manage to get public toilets into such a horrendous state in the first place - a complete lack of disrespect
I think there was also a problem with a lot of local characters 'consuming purchases' in the toilets. The station isn't in the most affluent part of the town, and the town suffers the same drug related problems as many seaside resorts with very seasonal economies.
There is invariably a SWR service sitting at the station unlocked (often two), so the advice to use the onboard toilets, whilst not ideal, does make some sense. As the 444s have 5 coaches, there should be at least one toilet which isn't too grotty.
Agreed about the way people use public toilets - but that's a societal problem which isn't easy to solve. Weymouth station could really do with ticket barriers as the user numbers seem a bit low, suggesting fares aren't being paid (not necessarily evasion given there are many unstaffed stations nearby). If it got them, it might be possible to put a portakabin on the platforms or similar. Again not ideal but better than nothing.
Back o/t, Filton Abbey Wood and Digby & Sowton lack toilets or any nearby facilities, although the former is constrained by the MoD buildings next door. The latter has a lot of rugby crowds - I imagine waiting for a late running train after a game isn't much fun given many people may be well refreshed.