NEW YORK—Commodities tumbled further on Friday as the U.S. dollar regained more ground, a sign that the cost of necessities like gasoline and groceries might take less of a toll on Americans’ budgets.

The dollar has, at least for now, clawed back from the losses it suffered this year. The U.S. Dollar Index on the Chicago Mercantile Exchange—which measures the dollar against a group of world currencies—rose to levels not seen since late December 2007. That trend has lessened the allure of using dollar-denominated commodities as a hedge.

The greenback’s comeback has hit g...