I've got an old Flying Magazine (circa 1970 or so) where one of the editors
makes the comment that it is better to take off overloaded (with fuel) than
it is to try a launch with marginal fuel in order to stay under gross. The
comment was the same... It'll fly better over gross than outta gas.

I bet the magazine's lawyers wouldn't let them print that now...

Don't tell anyone... but I did that almost routinely training for my
PPL. We were flying an old, tired C-150 in a Georgia summer (which
automatically means density altitudes are incredibly high). I weighed
about 180 at the time; my instructor was about 240. We were usually
over gross by about 40-50 lbs, and when flying dual we were lucky to
get 250fpm out of it.

My examiner was even bigger... I had to check the fuel levels and set
it up so that I'd burn enough on the way over to his airport that we'd
be right at gross for the checkride... which meant coming back home
afterwards was cutting it close (but then, it's only an 11 mile
flight).