I don’t believe there’s a more concrete answer on this, but I’d say it has to do with a depiction of his ability.
Mewtwo is known as possessing immensely powerful psychic abilities. Typically, “psychic abilities” gives a sense of gracefulness and floatiness when you think of levitation and telekinesis (abilities important to Mewtwo). This is shown in Mewtwo’s actions through not only his unusually light weight, but his floatiness and slow movement and fall speed. A light weight also demonstrates that Mewtwo’s physical strength is not what defines it, it is its outstanding psychic power.
In conclusion, I would say it is as he is mostly getting around using his mental, psychic ability, giving the illusion of having low weight. Remember that the SSB series is also often inaccurate to the actual Pokemon series, they can create factual inconsistencies if they deem it will improve play.