Actually, it might be technically possible to have 'liquid metal skin' without any noticeable weight gain.
A lot of that can be determined from the type of metals used in the skin's compostion. There are metals and alloys that are indeed light, and if only replacing the skin, wouldn't represent a huge weight increase. I'm not a scientist, but titanium comes to mind as being durable and featherweight.
Another thing to consider is the nature of the power. Is the character's body so-called 'organic steel'? Technically, to be considered organic, the object--in this case, the person's flesh--must contain carbon.
Carbon in steel is nothing new--some of the strongest alloys available are tempered with carbon. Indeed, if you factor in nanotechnologies that we're developing in current science and extrapolate it to the Nth (aka comic science) degree, it's definitely possible. Carbon rods are being strung together in threads which have the tensile strength of steel many times over, while being a fraction of the weight. Partner that with a particularly light and durable metal--titanium, for instance, and you've got your 'organic steel'--which is both lightweight AND resilient.
I'm not arguing against injecting realism into games, and indeed I hope that provokes further discussion into putting bleeding edge science and philospohy to work in your games.