Hi & Welcome. I guess that you're Canadian too, eh? Where are you from?
Now, the tires. Did they replace all four? What kind are they? If they road test the car they'll likely feel the same vibration that you do. It's surprising to hear that a weight flew off - they really stick well to a properly cleaned surface and you shouldn't have had a problem, but if you've paid to have a job done and it hasn't been done well enough, take it back. Tire balancing isn't a hard job and if that's really the problem they should be able to correct it fairly easily.