Are you on the latest version of PyTorch (1.3)? We made some changes to significantly decrease the size of TorchScript binaries. For mobilenet_v2 on the nightly version of PyTorch, I get very similar sizes between eager PyTorch and TorchScript:
$ ls -la --block-size=M
-rw-------.  1 user user 15M Nov 15 13:06 net.pt
-rw-------.  1 user user 14M Nov 15 13:06 net.pth

If you are on PyTorch 1.3 and still are getting this problem, could you try using the nightly PyTorch package and see if that fixes it?