Filter only with capacitor
Your distortion is due to source unable to drive as much current  for positive waves.
But I will not guess your source.

All capacitors uses electrodes and the surface area and chemical bond determines the effective series resistance , which can load AC waveforms which changes the slope of the voltage and the peak amplitude. 

Usually that's a good thing but it all depends on the driving current-limited source-resistance ratio to load capacitive impedance and it's internal ESR.







simulate this circuit &ndash; Schematic created using CircuitLab

Although I could guess why out positive wave slope reduces with higher resistance, let's see here how Vpp and Ipp changes at some arbitrary low frequency and fixed series resistance.