Is it normal to have wheel weights attached in two different locations after being balanced?

I got my wheels balanced a few weeks ago and there is a bit of adhesive left over from a strip of weights that were attached apart from the strip that is currently in place. I don

 

That sounds possible. They balance the tire/rim combination. Most weight distribution imperfections in a rim/tire combo are found in the tire part assuming you have some quality rims. If you got new tires since the last time they were balanced the weights could easily need to be moved.