True, *if* those are the lenses you'd use on each.
But the camera body is no heavier -- for example, the d750 is actually lighter than the d300. In fact, the d750 with 28-300 may be lighter than d300 with 18-200.
But also, as I said, it's just a matter of reach. I rarely ever need 300mm. I never ever shoot with super zooms. I'd mostly be using the same lenses, regardless of whether fx or dx, just with less reach. I'd be packing my 70-200, my 50/1.8, either way. The only dx lens I'd pack would be wide angle.
So yes, absolutely easier to get long telephoto reach on aps-c with a lighter package. But if you're not shooting telephoto much.... What is the reason to avoid ff?