If anyone is interested.....I spent some more time googling and finally tracked down the name of the weedy vine that has been plaguing me. It's Polygonum perfoliatum, mile-a-minute vine, also known as Devil's tail tearthumb; both common names give a pretty fair description of what it's like.
It was originally introduced into this country in the 1930's with a shipment of rhododendrons into a nursery in York County, PA, and has spread from there. Since I am in the next county over, it's no wonder I see it around everywhere.
There's a good article on it here:
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, Sue