Weber doesn't have the stones(like Scotty Stevens) to lead his team to success so he wants to be a passenger on another team. He probably also wants a bit more glitz and glamour.
Weber is one of, if not the, only defenseman in the game right now worth doing this for. Can't downplay Weber here. He is that good.
Stevens didn't want to be here at first. It took him a while to become the player he did here.
I don't see much value with four 1st round draft picks that will probably somewhere around 25-30 each year. They could sign him and get a lot more value than that, probably from the Flyers themselves.
They can't move him for a year if they match. If Weber is intent on leaving, it wont be good to do that. I think it would be smart to match it just based on that, but I really can't see them doing that unless he's just trying to force Nashville into the long term contract.