The weight of gemstones is universally described in carats where 1 carat = 0.2g.
Should you be in the fortunate position of trying to decide between buying either a 1 carat emerald or a 1 carat ruby of the same shape (now that would be fun!) and looking at them side by side, don’t expect them to be exactly the same size…
Ruby is a denser material than emerald meaning its atoms are more tightly packed together. This means that a 1 carat ruby will be physically smaller than a 1 carat emerald.
A couple of other examples of denser, heavier materials would be pyrite or gold while less dense, lighter materials would be jet or amber. Away from the jewellery world, consider lead and polystyrene as density comparisons – if you had a 5cm cube of them in either hand for comparison, you would definitely be able to tell which was which with your eyes closed. Density is about the weight of a material relative to its volume - love a bit of science!