Common-Emitter Behavior
It's a bit hard to say, given that we can't see any of the scope settings (vertical or horizontal).

But the waveform you're showing is a characteristic of how the emitter bypass capacitor gets charged and discharged. The charging impedance (through the transistor) is much lower than the discharging impedance (through the resistor). As you drive the base harder, the charging current goes up (faster rise time), but the discharging current cannot change (same fall time).

Bit what this really indicates is that the emitter bypass capacitor is too small for the signal frequency &mdash; the voltage should not be changing significantly at all. Either pick a higher signal frequency or use a larger bypass capacitor.