While a 4X scope may be sufficient for hunters under short range situations, the 3x-9x variable scope gives a hunter/shooter much greater flexibility and is the most popular scope sold, according to an article I recently read.
As concerns the difference in weight, I believe you'll find that really isn't much a factor. There is a greater difference in weight between my heaviest and lightest rifle slings than between my heaviest and lightest scopes.
Whatever scope you decide to use for hunting is the scope you must "sight-in" with... obviously. The 3x-9x variable scopes are the most popular scopes because they tend to give the "best-of-both-worlds"... 3x magnification for close shots, 9x for long shots and your choice of magnification for the all the shot in-between.
If you're trying to determine what "load" is best for your rifle, then the most powerful scope you can mount on the rifle is the one you should use. I like use my varmint rifle's 6x-24x variable scope set on "24x" on a different rifle when I'm working up loads for it. The better you can see the bullseye, the more accurately you can "hold" on it... all other things being equal.
Of the six hunting scopes I have on my rifles, four of them are 3x-9x variable scopes including the scope on my Model 99 Savage in .300 Savage caliber I use for eastern deer hunting.
If you hunt where the average shooting range is 150 yards or less, I would recommend you look at a 1.5x-4.5x variable scope like the one I have mounted on my old model Ruger .44 magnum carbine that makes a really great "still-hunting" rifle/scope combination. When I was "still-hunting" through the woods or even when on "stand", I kept the magnification turned down to 1.5x in case I needed to get off a quick shot at close range. Looking through the 1.5 power scope is almost the same as looking through no scope at all and the very heavy crosshairs that thin down to "wire-like" crosshairs at the center helps "guide" your eye to the center of the crosshairs and automatically causes you to "center" your target between the very heavy, "post-like" crosshairs "sprouting out" from all four sides of the scope.
If the deer is far enough away that you need more magnification, then the deer is far enough away that you can afford to take the time to turn the magnification up to "4x" if you need it.
While a fixed power scope at any "power" may be slightly lighter in weight than a variable power scope, the variable power scope has mostly replaced the fixed power scope due to the obvious advantages the variable power scope offers.
As far as what scope to use for hunting, a lot depends on where you hunt and the range you can reasonably expect to get shots at deer. If you hunt in an area like much of the eastern USA where most shots at deer at taken at less than 100 yards, a 4X scope would do just fine. If you hunt out west or in the "bean-fields" of south-eastern U.S. where shots tend to be much longer, the 3x-9x, 4x-12x or even a 5x-16x variable scope would probably be the better choice.
Therefore, depending on the average shooting range your type of hunting requires, I'd go with the variable power scope in the power-range of your choice.