The technique for analytical investigation of the Alfvén resonance, proposed by Dmitrienko [J. Plasma Phys.57, 311 (1997); 62, 145 (1999)] is used to obtain the matching conditions and to calculate the rate of resonant absorption and heating in a nonlinear dissipative resonance layer. It is shown that one matching condition is the invariability condition for the coefficient of the singular part of the solution describing the MHD mode outside the resonance layer, and the other condition is a jump of the coefficient of a regular solution, the value of which depends on the ratio of the dissipative to nonlinear spatial scales. It is established that the ratio of the jump of the imaginary part of the regular solution to the coefficient of the singular solution is exactly equal to the rate of resonant heating, and this heating is calculated as a function of the ratio of the linear dissipative to nonlinear scales. The resonant absorption coefficient is calculated as well. It is shown that the nonlinearity leads to a decrease of the heating rate and the absorption coefficient compared with those predicted by linear theory.