Adamantium's durability has less to do with weight than it does with resilience. Logan is 5'3" tall and without his adamantium weighs 195 lbs. With it, he weighs 300 lbs. His body has been reinforced but adds only 105 pounds of total weight.
It is wrong to assume its indestructibility is related to weight. There are plenty of heavy metals (gold, lead) which are very dense at the molecular level, but incredibly soft. Iron and titanium are both less dense than gold but are far stronger.
Adamantium's structure (defying the laws of physics as we understand them) once its form is set, it simply resists any form of physical transformation without an expenditure of cosmic forces, matter reorganization, or powerful magic.