I have an Entry Form and a GridView on the same page. Selecting a row from the GridView populates the TextBoxes in the Entry Form above it with all the entries of the GridVi
As stated in all posts, you can do some form of compression in multiple ways, you can implement it yourself or buy a viewstate compressor, but that won't help you too much. What might be interesting is the amount of compression you should expect. Take a look at: RadCompression to gets some info on compression rates, and performance improvements that are generally the same for all choices (free/paid).
My opinion that rates are not satisfactory, and you should look for design alternatives for your problem.
Now, if I understand correctly you want to edit a grid row in a form on the same page. From the comments, you are using an update panel, and by the behavior described you have both your grid and edit form in an update panel. If your page has only the grid and edit form, having them in an update panel won't help at all.
I've made a small example for test purpose and I had a 10 rows grid with 5 columns and an edit form for the 5 fields on the same page. My observations are:
That's because using an update panel basically means that you are not refreshing the entire page, but only the area inside your updatepanel + viewstate. So, if all your page is surrounded by the update panel, that won't help you at all, and it's not fair to call it AJAX :).
Now, asp.net web forms has it's strengths but my opinion is that nobody likes asp.net web forms anymore, especially when having asp.net mvc / wcf / jquery at hand. Your question proves one of the limitations of asp.net web forms when used as originally intended.
My general solution for your problem would be: