It'll be heavier than an Earth-like world the same size but we can't actually work out how heavy.
Carbon Planets aren't really made of carbon, they just have enough carbon, as a molar fraction, that it can't all react with the available oxygen and hydrogen so you can get pure carbon that can't be oxidised into CO, CO2 or the CO3-2 Carbonate ion or converted into simple organic compounds like CH4. So as well as borate, carbonate and silicate rocks, which will be holding most of the world's oxygen, there would also be some borides, carbides and silicides but not necessarily in large volumes and they'll tend to be in the mantle as they're much denser than their oxygen bearing counterparts.
Given the rarefaction process that needs to occur to form a Carbon Planet they're going to be quite dense, since they lack not only hydrogen and oxygen, and thus water, but also light halogens and also some of the lighter metals like lithium. There will be relatively more heavy metals and more of them will be in their pure (unoxidised) state so they'll pack together tighter under pressure, especially when hot. The mantle will be denser so the diamond belt (this is about 900km down on Earth), where diamond becomes the most stable form of pure carbon, will be closer to the crust but they're a bit less likely to migrate to the surface because the mantle is denser.
Overall mass is impossible to make an exact quantitative call on; the world will certainly be denser than Earth but it already would have been because it's bigger, therefore more massive, and therefore has higher core pressure and density. It will also have a higher pressure/depth gradient due to the reduced level of oxygen in the mantle increasing its density. Density gradients are never more than estimates and have proved extremely problematic to calculate let alone predict based on composition. So we can't really work out a solid figure for the average planetary density and thus get a good prediction for total mass.