Umbrella-sampling (US) histograms, when they are reweighted by a factor dependent on the applied bias potential, provide information about free-energy curvature in individual sampling windows. These curves must be aligned (vertically shifted) to construct the total, smooth free-energy profile on the whole reaction-coordinate range.

In principle, you can do the alignment even when the curves do not overlap, but then you must extrapolate them or fit the biased histograms by some analytical function, for example by Gaussian curve like in Kastner's Umbrella integration method. However, accuracy of these approaches decreases rapidly when the overlap is poor or missing.

WHAM, on the other hand, does not align the PMF curves but it uses the least-square fitting technique to construct the total unbiased distribution from the biased US histograms. This is more accurate approach (with minimal statistical error), applicable also on multidimensional US simulations, but the histogram overlaps are really crucial for the fitting - without the overlap the iterative cycle in WHAM fails to converge and the free-energy surface has discontinuities. You can find detail discussion of  WHAM error estimation in J.Comput.Chem. 33, 453-465 (2012) or in original Kumar's papers.