(A) The resistance of a wire is given by the formula $R = \rho \frac{l}{A}$.
Where:
$\rho$ = Resistivity of the material of the wire.
$l$ = Length of the wire.
$A$ = Area of cross-section of the wire.
From the formula,it is clear that resistance is inversely proportional to the area of cross-section $(R \propto \frac{1}{A})$.
$A$ thicker wire has a larger area of cross-section,which results in lower resistance. Conversely,a thinner wire has a smaller area of cross-section,resulting in higher resistance.
Since current flows more easily through a path of lower resistance,current will flow more easily through a thick wire compared to a thin wire when connected to the same source.