Q.Japanese maple is only partially blooming
We live in Michigan and had very cold winter. The tree was wrapped in burlap, but only about 1/3 of it has come back. It is 6 years old, but we moved it and replanted it 3 years ago. This spring it is only partially blooming.

The harsh winter is most likely to blame for the current state of your tree. On some of the branches that don't have leaves you may want to conduct a scratch test to see if there is any sign of life in them. Guidelines on how to conduct a scratch test can be found in the following article: http://www.starkbros.com/growing-guide/article/how-to-do-a-scratch-test/ With a scratch test, "green is good" and means the branch in question is still alive and that it may make a comeback with a little time and patience.
Below are some articles that will help you which discuss leafing out problems on trees and how to diagnose them:
https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-leafing-problems.htm
http://extension.oregonstate.edu/gardening/how-examine-deciduous-tree-leaf-out-problems