The MSSM leads to precise predictions of the properties of the light Higgs boson degrees of freedom that depend on only a few relevant supersymmetry breaking parameters. There is an upper bound on the mass of the lightest neutral Higgs boson, which for a supersymmetric spectrum of the order of a TeV, is barely above the measured M_h = 125 GeV at the LHC. Raising this bound by considering a heavier supersymmetric spectrum has consequences for what can be observed at the LHC. In a previous article, we studied the variation of the predicted lightest CP-even Higgs mass for large values of the scalar-top and heavy Higgs boson masses. We perform a similar analysis, considering also the case of CP-odd Higgs boson masses of the order of the weak scale. We perform the calculation using effective theory techniques, considering a two-Higgs doublet model and a SM-like theory and resumming the large logarithmic corrections that appear at scales above and below the CP-odd Higgs boson mass, respectively. We calculate the mass and couplings of the lightest CP-even Higgs boson and compare our results with the ones obtained by other methods.