I notice that when Sam‘s Club rotated my tire and that they also check and rebalance each one. If rotate the tires myself at home, I have no way of balancing it. Do you need to check for balance or the tire should be ok. It is the metal weighted piece that you see on the tire rim. Each weight is different depending on how much weight is neeeded to balance the tire I think.
Not necessarily. At Sam's - if you purchased the tires there and bought the $10 service on each tire - then a rotation AND re-balance is part of the deal.
Tires occasionally need rebalancing whether you rotate them or not; there's nothing about rotation that makes rebalancing necessary. On the other hand, sometimes rotating the tires makes you notice an out-of-balance tire - for instance, if you have FWD, and a tire moved from rear to front suddenly makes the handling seem squirrelly.