The Ruger M77 Scope Ring Set 1 Inch Medium Blue 90410 should work with a Vortex scope with a 1" diameter tube and 44mm objective lens.
Ruger does not state the weight of the Ruger M77 Scope Ring Set 1 Inch Medium Blue 90410. However, from what information I could find the set weighs around 3 ounces. I recommend contacting Ruger to confirm the weight of the Ruger M77 Scope Ring Set 1 Inch Medium Blue 90410.
Ruger does not provide specific measurements for their Ruger M77 Scope Ring Set, but state the medium height will accommodate an objective lens up to 42mm.
As long as the scope has a 1 inch tube diameter it will work.
Yes it will.
Yes it will. They are Blue finished.
No, they will not. They will only work on M77's with Ruger's proprietary integrated scope bases.
No they will not, they are made specifically for the M77.
No, these are not the proper rings, they are only for a traditional M77 that uses two different height rings. For the 77/357 you will want standard Ruger rings like these here: https://www.opticsplanet.com/ruger-scope-ring-4b-medium-blue-90270.html
No, these are different heights for the front and rear ring to fit standard Ruger M77 calibers. The 77/22 requires two rings that are the same height. Here is a link to the correct ring, you will need two as they are sold individually:
https://www.opticsplanet.com/ruger-scope-ring-4b-medium-blue-90270.html