DHL weekend delivery is not available in North America.
DHL provides minimal weekend shipping services, keeping them for urgent packages and charging extra on top of it. However, the carrier might be the right solution for delivering out of the usual workweek if you ship within a few select countries like Belgium, the Netherlands, Luxembourg, or the United Arab Emirates.
If your business or its branch is located on one of the territories covered by DHL's Saturday Delivery service, be prepared to pay up to 50% extra. Here's a comparison for workday/weekend delivery of a compact package between German cities Berlin and Cologne (approximately 370 mi):