Actually, most nuclear weapons get roughly comparable amounts of their force from fission and fusion, usually a little more from fission. Fission-only bombs are so much less powerful not because fission is but because they have very incomplete fission (around 1% for the Hiroshima bomb design, for example). The fusion reactions used in bombs produce a lot of excess neutrons, by design; all those neutrons flying around mean a lot more fission ends up happening. The only bombs that get most of their power from fusion are neutron bombs (which use a lot less fissionable material, and use the excess neutrons to increase the radiation damage) and clean bombs (which also use a lot less fissionable material, but replace it with lead to absorb the excess neutrons; clean is of course a relative term here).