Let R be a Gorenstein ring. We first study Gorenstein orthogonal classes and Gorenstein cotorsion pairs of R-modules. Then, we introduce the concept of Gorenstein weak tilting R-modules, which is a “Gorenstein analogue” of weak tilting modules. It is proven that a left R-module W is Gorenstein weak n-tilting if and only if its character module W⁺ is Gorenstein n-cotilting if and only if its Gorenstein flat dimension is at most n and its left Gorenstein Tor-orthogonal class consists precisely of all right R-modules with a G-exact right Prod-resolution of finite length. Finally, we explore the connections between Gorenstein weak tilting modules and Gorenstein tilting modules.