A depreciation in the exchange value of the dollar should increase the dollar price of U.S. imports. In response, domestic consumers should purchase fewer of those now more expensive imports. If the quantity purchased (“real imports”) declines by a greater percentage than the price increased, then the total nominal or “current dollar” value of imports declines. So, a weaker dollar should reduce the total dollar value of imports.
Since its peak in 1985, the foreign exchange value of the dollar has dropped more than 50%. A fall that great should have dramatically reduced the deficit in U.S. international trade by now. It hasn't.