Suppose you made a sword out of diamond (just follow me here, it's only theoretical). Would it be lighter than a sword of the same size made out of steel?
Diamond has half the density of steel but would make a terrible sword because it is not very tough. Toughness is a material's ability to resist breakage from forceful impact: Diamond has a toughness of 2.0 MPa·m1/2 and has a critical stress intensity factor of 3.4 MN·m?3/2. That makes it tough for a gem but are poor compared with steels. Plus diamond has a cleavage plane.
The weight of steel is dependent among what kind of steel, shape, length, width, thickness a 5mm by 5mm ball of carbon steel would wiegh 1.69969 g a same size diamond weighs .79 carats equivelent to 1.5 grams So the basic answer is, yes, diamond is lighter than steel, but barely
Just compare the densities. The density of diamond is about 3.5g/mL. While there are different types of steel with different densities, steel is mostly iron, so the density of iron is a good approximation. Iron has a density of 7.87g/mL. Steel is over twice as dense as diamond, so the diamond sword would be lighter.
steel is heavier. 6.5 mm/1 carat of steel is 7 grams, while diamond is 1/5 a gram