  In the present paper we consider the regularizing properties of the repeated
midpoint rule for the stable solution of weakly singular Volterra integral
equations of the first kind with perturbed right hand sides. The H\"older
continuity of the solution and its derivative is carefully taken into account,
and correction weights are considered to get rid of initial conditions. The
proof of the inverse stability of the quadrature weights relies on Banach
algebra techniques. Finally, numerical results are presented.
