Why WebMethod declared as Static?
They're static because they are entirely stateless, they don't create an instance of your page's class and nothing is passed to them in the request (i.e. ViewState and form field values).
HTTP is stateless by default, ASP.Net does a lot of stuff in the background with ViewState, Session, etc. during a standard page request to make life easier for developers.
When a web method is called through AJAX, the page isn't sending all the necessary form data ASP.Net embeds in a page to keep track of request state because it would make web methods too slow; and if you need to do a lot of processing you should move it out to a dedicated web service instead.
You can get access to methods on the page using HttpContext.CurrentHandler which is explained in more detail here and also the current user if you need it via HttpContext.Current.User.
There's an excellent article here explaining this in more detail.