This BuddyPress plugin replaces the functionality for the Public Message and Private Message buttons on profile pages.
BuddyMessageUX-Free is a BuddyPress plugin.
Default behavior for the buttons is to take you to your own profile - to compose and send messages from there. Why? Why not stay on the profile page you are viewing?
Fortunately, BuddyPress makes it easy to replace the functionality for those buttons. With this plugin you can stay on a profile page and send private or public messages to that member.