My experience is that tire shops charge a couple bucks extra for balancing tires, and they don't do it unless you ask. And yes, the little lead weights mean that the wheel, with its tire, was balanced at some time in the past. However, even if they change the tire, I don't think they pull off the old weights unless the wheel and new tire are rebalanced, so you could be running with an improper set of balancing weights.
Once balanced, I don't think there is a need to rebalance them, but I'll defer an expert on the topic.
Bill
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