Are you familiar with a geostationary satellite? That's a satellite that orbits the equator at the same speed as the earth turns, so it's always over the same spot of land, 22,500 miles up. Could you let down a rope and pull up some supplies?
The answer was no, because no rope is strong enough to support its own weight at that distance. Before you even get a chance to tie something to the rope, it would snap - from trying to support thousands of miles of rope!
Well, what could you do? Maybe you could have the rope gradually become wider as it goes up.
Think of it this way. A one-inch-wide rope would break with a certain weight, but a two-inch-wide rope could hold that weight. Why not figure out what the maximum possible weight is at every point along the rope, and have it be just a little bit wider than the breaking width?
Sounds good, but what are we forgetting?
Think for a second.
Yep, every time we widen the rope, we also increase its weight. Any benefit we gain in being able to hold what's under a certain section of rope would be canceled by the added strain of holding that section.
Aside from that, to reach all the way to a geostationary satellite, the rope would have to be thickened so much that it wouldn't really be a rope any more. It would wind up being about three hundred feet wide at the top, even if the bottom end were a tiny thread.