Thanks for all these rose suggestions. I've been on helpmefind.com pretty much every time I've touched my computer today. They don't have "weeping" as a search criteria, but they do have "ground cover" and "hanging basket" under the "Growth" search refiner.
I will be glad to post pictures of the results of my decision (pretty pillars, I hope!) this season. Glad to meet you all, and thanks again.