cheapest way to send heavy package depends on the destination and size of the package. USPS Ground Advantage is often the most affordable method for heavier shipments within the U.S., while FedEx Ground or UPS Ground might be cheaper for larger, heavier packages. For international shipments, options like USPS Priority Mail International or economy services from FedEx or UPS are generally more cost-effective than expedited services. Always compare rates from different carriers to find the best deal.