Aside from the sheer weight of the load, what is the main reason that she sled won't move when the dogs try to pull it?

The sled won't move because its runners are frozen in the ice.

“It’s not that I care a whoop what becomes of you, but for the dogs’ sakes I just want to tell you, you can help them a mighty lot by breaking out that sled. The runners are froze fast. Throw your weight against the gee-pole, right and left, and break it out.”