Can you stop a willow from weeping?

The short answer is "no." The weeping habit of the tree is inherent to the species. The common weeping willow is a hybrid species called Salix x sepucharis. If you want to plant a willow tree that doesn't weep look for other species, such as white willow (Salix alba), black willow (S. nigricans), violet willow (S. daphnoides), or purple willow (S. purpurea).