Why are relative atomic masses used rather than actual masses of atoms?

The concept of relative mass was developed well before the actual masses of atoms could be determined. Also, as was pointed out, the actual masses are very small values. it is much easier to use relative masses in calculations as well as easier to print and to remember.

The actual masses of atoms are too small. For example, the actual mass of one carbon atom is 0.00000000000000000000002 g

experimentally atomic masses (in a.m.u.) are measured as a ratio with respect to a standard atom (the C-12 atom)

In most cases you need the average mass. The atoms of the element are a mixture of isotopes.