Catching a barbell any lower than you have to is a contrived movement--like Bobby says, to do so, you have to ease up on the pull, etc. I don't think this is always a problem, but in your case I would hesitate to recommend it.
Work on your snatching as you are, add in heavy snatch balances and snatch push press + overhead squat to get used to being down there with tons o' weight overhead, and get down there when you need to snatching.
You may have been implying this when you said 'drive', but make sure you're actively pulling yourself under the bar. The heavier the weight is, the more inertia, so the more you'll be able to use it as an anchor to 'muscle snatch' yourself under it.
All that said, it's entirely possible to perform a complete snatch with a very light weight--just takes discipline with the pulling power and very precise technique.