How does resistance change with thickness of the wire?
A thicker wire (of the same material) has lower resistance.
Having a thicker wire means that the volume of conducting material has increased so there are more conduction electrons available.
A concrete example of this point would be consider the current that flows through a wire. Now take a second identical wire and set it parallel with the first. The current that flows through the parallel combination would be larger (by a factor of two). Therefore the resistance of that arrangement must be less than the single wire (half the resistance of the single wire).