We report the measurement of spin waves in the bilayer colossal magnetoresistive manganites La2-2xSr1+2xMn2O7 with x = 0.30, 0.35, and 0.40. For x = 0.35 and 0.40 the entire acoustic and optic dispersion relations are well described by those for a bilayer Heisenberg Hamiltonian with nearest-neighbor exchange only, which is explained together with the spin-wave lifetimes by the double exchange model. The in-plane exchange depends weakly on x, but that between the planes of a bilayer changes by a factor of 4, directly revealing a change from mixed d(3z(2)-r(2)) and d(x(2)-y(2)) orbital character to mostly d(x(2)-y(2)).