The information sent to the server is safe and can't be accessed by anyone, not even by the server. It is password protected.
Weave connects to the server each certain intervals of time depending on the user needs. If you only access it from one computer it connect each 24 hours, if you access from more than one computer, it will connect several times a day.
Weave is a very interesting add-on for Mozilla Firefox that allows you to enjoy your settings from different computers.