As always, the answer is both no and yes.
For starters, the M1 really hasn't got any heavier. There's a lot of discussion that the TUSK upgrade has made them a lot heavier, but there is really no such thing as a TUSK upgrade. The TUSK upgrade is simply a collection of enhancements that can be added if the situation dictates, very little of it is a permanent addition. The things that will add considerable weight - the ERA tiles and slat armour - are simply sitting in a warehouse somewhere waiting for the big one. If weight was a concern due to the tanks being deployed by landing craft, the TUSK enhancements could simply be attached onshore.
At the moment, the LCM1E can carry an M1 but only in sea state 2, although that is largely due to seaworthy regulations unique to Australia that I don't really understand. The constraints make deployment of the M1 by landing craft difficult, but not impossible. Of all the problems with the development of the amphibious capability, deployment of M1 is one one of the minor ones.