Is this the one you're talking about
If so, the blah-blah at top says that the dk weight yarn (knit to recommended gauge) is what gives this pullover its drape, so . . . it sounds like the specified yarn in that
gauge is pretty important to the overall look.
With that said, you can try swatching up some heavier yarns and see if you get the drape you want. But it seems to me you'd also have to knit a swatch of the recommended yarn
to have something realistic to compare it to.
If it were me, I'd stick with the recommended yarn because the drape is vital to how this pullover looks and behaves. If you're going to splurge on the yarn, I say get the best one you can--the one called for in the pattern.