As far I as I know, and from naturalness considerations, a 125 GeV Higgs mass is rather large for the MSSM. This is because in the MSSM $$m_h^2 \lesssim M_z^2 \cos^22\beta + \Delta$$ where $\Delta$ represents top/stop loop corrections to the Higgs. It takes the form $$\Delta \sim \ln(\frac{m_\text{stop}}{m_\text{top}}) + \text{mixing}$$
Moreover, the Z mass is determined by the Higgs mass parameter, $m_{H_u},$ and $\mu$ (in the large $\tan\beta$ limit. i.e. $\tan\beta \geq 10$). And $m_{H_u} \sim - m_\text{stop}$, so the larger $m_\text{stop}$ the larger the fine-tuning in the MSSM. Now, only by large $m_\text{stop}$ (and mixing) one can reach a Higgs mass greater than LEP/LHC bounds. But this is already associated with large fine-tuning as I said.
So, in this view, a 125 GeV Higgs mass is large for the MSSM. (At least for the cMSSM.)
However, I realised that some people think 125 GeV is much less than what the MSSM predicts! Now this I don't understand at all. So could someone please explain what this view is based on?