Shipstation's App through BigCommerce is quite flawed. It does not allow method-specific rules to apply on the checkout, so orders are offered all shipping methods at checkout. For instance, first class is offered on shipments that are over 1lb and Fedex is offered for ship to locations with PO boxes.
Because Shipstation and BigCommerce seem to be big partners, I think there should be a way for Shipstation to specifiy shipping methods by weight, address type and restricted product on the front end checkout page.