I think the fundamental problem with the guessing going on about the Russian stuff is that all the Remainers think that the Russians were trying to induce a Brexit result. We can't know that - we can't determine their aims full stop.
I would assume the reasoning goes something like:
* The UK is, for now, one of the senior partners in the EU; it's one of the three largest economies, along with France and Germany, has the largest military after France and Germany, and is one of only two nuclear-armed powers, along with France.
* It's a major NATO member state.
* It's the European country with by far the closest cultural and political links to the USA, for obvious reasons, and forms a sort of bridge between North America and continental Europe (and much of the wider world - Australia/NZ, Hong Kong, etc).
* The UK leaving the EU weakens both parties, and by extension weakens links between the USA and Europe, which weakens "the West" in general.
* Anything that weakens the West strengthens Russia by default.
Not exactly rocket science.