An iceberg and a system consisting of the water equivalent of the
iceberg (the same number of molecules) have different masses, the
melted phase being the more massive of the two by an amount given
the internal energy difference divided by the speed of light squared.
Are you being cagey by using "weight", Jim? That just complicates
the question. The important conceptual point is the mass difference.
In the same uniform gravitational field (or equivalent thereof) the
water will evidently weigh more than the iceberg.