How do capacitors help in smoothing potential difference from a full wave bridge rectifier?
The charge time of the capacitor is hardly affected by load resistance at all (except in extremes). The charging of the capacitor is determined by the resistance of the forward conducting diodes in the bridge rectifier - this resistance is likely to be around 1 ohm or less.

The discharge time of the capacitor is determined only by the load resistor which is probably many ohms hence charge and discharge times will be different.

A more exact answer would consider the leakage inductance of the transformer feeding the bridge and the cable resistance feeding the transformer but, in general, the equivalent forward resistance of the diodes in the bridge ensure the cap charges quickly (compared to the discharge due to load resistance.

Here's a picture that shows an applied AC voltage and a single diode charging up a capacitor: -



After a few cycles of AC the capacitor is starting to receive full charge. Remember the picture is a half-wave rectifier so the negative excursions of the AC aren't contributing. With a significant load resistance there will be a droop/decay on the capacitor voltage between conduction periods of the diode but, under normal circumstances the voltage will have a trend that is asymptotic with the peak AC voltage minus 1x diode volt drop of about 0.7 volts.

Here's a picture that shows the droop in the capacitor voltage between diode conduction periods. This is a full-wave picture and assumes the diode is perfect: -