Joining the EU was not what Russia opposed, I think Putin even stated that he has no issues with that, it was joining NATO what Putin considered a security thread. So you have to think about the consequences of Ukraine joining NATO.

There are NATO nuclear weapons in Turkey, I don't know where exactly, but Turkey is as little as 170 km (100 mi) from the Russian border, separated only by Georgia, which is also supposed to become a NATO member according to the Bucharest declaration. So is it really that hard to imagine that Russia might be worried about nuclear weapons at their borders?

And I am no expert, I am not sure what kind of assets would be of the greatest concern, maybe it would be anti ballistic missile system weakening your nuclear posture, maybe it would just be a large number of tanks. So don't focus too much on me saying nuclear weapons but think more broadly about military assets in general.