Imagine it as a boxing match, your going to get hit, but winning is about where and how hard you/the enemy hit. For a lighter boxer to survive against a heavier fighter he HAS to move and avoid a knockout punch being landed.
A Medium is around half the weight of an Assault, but usually anything up to twice its speed and manouveranility, its likely that the Assault will punch the Medium out with a couple of well placed blows, if it gets the chance.....However a unmodified Kodiak (100tons) would have a significant disadvantage in a frozen tundra fight against an Uziel (50tons). The stock Kodiak has only an ERLLaser for range firing, the Uzi has twin PPCs, without cover there's no-way that the Kodiak could close on the Uzi (who will fire at max range and run away, recharge, cool down and repeat).
So it comes down to tactics and pilot skill, but I've seen many career Assault pilots (yes, I'm looking at you Daishi lovers out there) come to grief with a 'mech half their size throwing TBolts or PPCs from range and disappearing.
EDIT: What I forgot to add was I don't see any reason why MW:LL would change this fundamental of 'mech vs 'mech tactics