Why resistance of load resistor determines gain of common emitter amplifier?
So why we are calculating gain by dividing load resistor by emitter
  stabilizer resistor


What you can reasonably say about a common emitter amplifier that uses an emitter resistor: -


The collector current and the emitter current are broadly equal in value for DC and AC signals.
The AC (or signal) voltage at the emitter (across the emitter resistor) is very close in value to that signal voltage on the base (\$V_B\$)
The AC (or signal) part of the emitter current is therefore the signal on the base divided by the emitter resistor (\$R_E\$). This is ohms law (I = V/R)


So, given that collector current is the same as emitter current (DC and AC) and we know that this current is: -

$$\dfrac{V_B}{R_E}$$

That then allows us to predict the signal voltage |magnitude| on the collector because it is that current multiplied by the collector resistor, \$R_C\$: -

$$V_C = R_C\cdot\dfrac{V_B}{R_E}$$

Therefore the voltage gain (magnitude) is: -

$$\dfrac{V_C}{V_B} = \dfrac{R_C}{R_E}$$