Dear Student
The current will flow more easily when thick wire is used of same material. As resistance offered by the thick wire is less than that offered by the thin wire because resistance of wire is inversely proportional to area of cross sectional of wire in which current flows.
R (resistance) = p (density). l (length) / A (area of cross-section or thickness of wire).
So as area of cross-section ( or thickness) of wire increases, resistance decreases and more current flows through it.
Regards