are a couple of factors. The two biggest are the weight and density of a package. Airlines generally have a single fee for a checked bag up until 50 pounds (and that may vary).
Shipping companies charge based on distance, service and weight. To keep people from shipping feathers everywhere, shipping companies calculate dimensional weight and compare it to actual weight. The charge is for the higher weight of the two. This is easy to calculate. Just multiply the height, length and width in inches and divide by 194 to calculate dimensional weight.
The transit time from Minneapolis is three days for a ground movement which is the cheapest. Dropping off at a provider location will save a pickup fee.
You're probably looking anything over 20 pounds as better to check your luggage. If tou have an association such as an American Express card you could get a 10%-15% discount.