Weight doesn't affect the glide distance as the 2 factors that do affect the distance are lift and drag. Where the resultant from L and D is the best glide angle.
I'd like to make a slightly pedantic comment :
This is true only if the lift and drag coefficients are constant, which might not be exactly true. For gliders, it has been shown that the maximum L/D increases by a few percent with increasing wing loading.
Fact is that given the small chord length and low velocities, the Reynolds number (in the 700 000 range) is at the lower boundary of "developed" turbulence.
This is even worse for ultralights and models as shown
here
On the other hand, the constant Cl and Cd assumption is indeed valid for airliners, where Reynolds numbers are at least an order of magnitude higher.