Is yours one with chambering? Mine is a rather pretty 2005 Standard, which as I understand it was the last year without. Much to my surprise it isn’t that heavy, we went through this prior to the thread split, though I can’t remember exactly what it weighed (it was actually at the lighter end of LPs), but it really will not stay put on my knee the way I play it. My Gordon Smith is just the same. I joke about it, but I do find it a barrier to playing them as I have to keep my thumb wrapped around the neck to keep it down. They are both fine on a strap, but that just isn’t how I play. The Yamaha and Strat both balance perfectly.
PS I keep meaning to stick an advert up here as I think it is time to move a few guitars on. Potentially Fat Lester, the Gordon Smith GS1, the AVRI Jazz Bass and just maybe the Dan Smith Strat are up for grabs! I do definitely like the latter, but I would swap it for a similar value Strat with a whammy bar as being a hard tail it is just too close to my Yam SC1200 (except to my taste not as good). I’m actually starting to think about jazz-friendly semis or hollows. I rather fancy trying a 335 or one of the smaller variants and would certainly swap Fat Lester for one. I’d not turn my nose up at a proper Japanese-made Yam or Ibanez semi either.