Variable Weights

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I know that shopsite does not allow for variable weights. I have a problem that I can't figure out. I'm dealing with products that can ordered in custom cuts. So I have created a javascript function that figures the price and passes that number to the shopping cart. It works great. My problem is with shipping. I can I use UPS to figure weights when the weights are dynamic. Can anyone think of how I can figure shipping cost on the front end and then pass it to the shopping cart as a total price? Or how to pass a weight to the shopping cart.
Thanks in advance