There is a way to get underweight mechs through customisation, but only if they don't carry maximum armour.
What you do is increase their armour tons until their nominal weight is filled up, but then you don't assign the points to any location. This will not take extra time, cost extra money, increase the refit class or use up any resources (only actually changing the armour points in a location does that), but of course it isn't possible if you can't up the armour tons by enough to make up the difference.