If Hipshot lists weight on their site, I can't find it.
I did find that
birdsongguitars lists the weight of a
set of 4 Ultralights (they use the "Y" style) as
5oz.
I don't know if that includes screws and bushings or not, and I also don't know how that relates to the cloverleaf style ultralights.
I weighed
all 4 of the stock tuners off my Geddy, no screws or bushings, at about
15 oz! (3.8 oz each). Screws and bushings only add about another 1 oz.
That's a big difference, and I would expect that it would really help your problem... probably fix it completely, like Depalm said.