There are two different types of weighted ropes - weighted grips, or weighted rope, or a combination of the two. A weighted grip forces you to still maintain the flick and speed to get a lightweight rope around, but fatigues your shoulders and wrists more due to the weight of the handle. A weighted rope will come around easier due to the inertia of the weight, but long sets will be extremely fatiguing due to maintaining position. A combined rope does both.
Heavy rope:
http://www.roguefitness.com/rogue-heavy-jump-ropes
Combined rope:
http://www.roguefitness.com/rogue-pro-jump-rope
Evil rope:
http://www.roguefitness.com/outlaw-120-ropes
Thick ropes shouldn't be an issue depending on the surface. They recommend to use rubber flooring, but non-abrasive concrete would be fine too (might get cool sparks too if you have an uncoated rope!).
If you get a reasonable set of weighted handles you can always get additional wire to swap out what type of rope you're using.