I've seen it full and standing on a Saturday.
I've used the line occasionally, although not since Covid, and as I recall, I used to see some fairly busy trains and some very empty trains. I don't think the busy trains were only in the peak hours.
Trying to be a bit more scientific about it, official station usage stats (from Wikipedia) are: Morecambe 0.165 M (M=million), Bare Lane 0.113M, Heysham Port 0.009 M. That adds up to 0.287 M. That makes 788 journeys a day. A quick check on the timetable says, 26 return train journeys Mon-Fri, 25 Sat, 12 Sun which works out at an average of 24 tpd each way. So that makes an average of 17 passengers on each train.
There'll be some double counting in that figure - because I've counted anyone travelling only West of Bare Lane twice, but on the reasonable assumption that most journeys are to Lancaster or beyond, that number won't be that far out (and on the other side ticketless journeys are not accounted for, and also not accounted for cancelled trains/engineering works etc.).
On another note, I realised looking at the timetable that trains are timetabled to take 15 minutes from Morecambe to Heysham Port, a distance of 4.3 miles, making the average speed 17.2 mph with no intermediate stops. (Before anyone objects, I've excluded the 3 minutes dwell time at Morecambe - public timetables show 18 minutes). Does that track really have such a low maximum speed? I think if we want to provide a couple of intermediate stops to get regular passengers from Westgate/Heysham, you'd need to do something about that.