The thicker the wire the more current that can pass through the wire. It is similar to a water hose (1/2 inch) a smaller hose will pass less water than a thicker (5/8 inch) hose in the same time frame.
Why Does The Thickness Of The Wire Have An Effect On The Current?
The current flowing in a wire is inversely proportional to its resistance which in turn is inversely proportional to the cross-sectional area of the wire. Hence thicker the wire,more is the current flow.