We can't determine why some of the trunks and branches are dropping by viewing the photos.

However, wind, heavy rain, and rapid new growth may account for the droop.  So might insect and/or disease damage. 

Some birch species exhibit a weeping growth habit. That characteristic may have been exacerbated by one or more of the above mentioned factors.

Whether and to what extent the drooping trunks and branches will right themselves remains to be seen.

In the meantime, consider asking a certified arborist to assess the tree's health on site and recommend a course of action.  If remedial pruning is needed to improve the tree's form, an arborist will be able to provide that service. 

If you decide to hire an arborist, the following information may be useful:

https://extension.umn.edu/planting-and-growing-guides/how-hire-tree-care-professional

Here is a reply to a similar question:

https://ask2.extension.org/kb/faq.php?id=260004