The nucleus made by fusion is heavier than either of the starting nuclei. However, it is not as heavy as the combination of the original mass of the starting nuclei (atoms). This lost mass is changed into lots of energy. This is shown in Einstein's famous E=mc2 equation.
Fusion happens in the middle of stars, like the Sun. Hydrogen atoms are fused together to make helium. This releases lots of energy. This energy powers the heat and light of the star. Not all elements can be joined. Heavier elements are less easily joined than lighter ones. Iron (a metal) cannot fuse with other atoms. This is what causes stars to die. Stars join all of their atoms together to make heavier atoms of different types, until they make iron. The iron nucleus cannot fuse further because of its high nuclear binding energy. The reactions stop. The star eventually cools and dies.
On Earth it is very difficult to start nuclear fusion reactions that release more energy than is needed to start the reaction. The reason is that fusion reactions only happen at high temperature and pressure, like in the Sun, because both nuclei have a positive charge, and positive repels positive. The only way to stop the repulsion is to make the nuclei hit each other at very high speeds. They only do that at high pressure and temperature. The only successful approach so far has been in nuclear weapons. The hydrogen bomb uses an atomic (fission) bomb to start fusion reactions. Scientists and engineers have been trying for decades to find a safe and working way of controlling and containing fusion reactions to generate electricity. They still have many challenges to overcome before fusion power can be used as a clean source of energy.