Using scanning tunneling microscopy, we study the post-deposition coarsening of distributions of large, two-dimensional Ag islands on a perfect Ag(100) surface at 295 K. The coarsening process is dominated by diffusion, and subsequent collision and coalescence of these islands. To obtain a comprehensive characterization of the coarsening kinetics, we perform tailored families of experiments, systematically varying the initial value of the average island size by adjusting the amount of Ag deposited (up to 0.25 ML). Results unambiguously indicate a strong decrease in island diffusivity with increasing island size. An estimate of the size scaling exponent follows from a mean-field Smoluchowski rate equation analysis of experimental data. These rate equations also predict a rapid depletion in the initial population of smaller islands. This leads to narrowing of the size distribution scaling function from its initial form, which is determined by the process of island nucleation and growth during deposition. However, for later times, a steady increase in the width of this scaling function is predicted, consistent with observed behavior. Finally, we examine the evolution of Ag adlayers on a strained Ag(100) surface, and find significantly enhanced rates for island diffusion and coarsening.