We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as . Meanwhile, the energy spectra of incompressible components display the same scaling of as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.