Evidence is all about correlation. You won't ever find direct causation in a court case.

That's what a jury is for.

It's part of a greater collection of evidence. Evidence doesn't have to be mathematical proof.

A common theme (from what I can tell in law) is that something can never be proven to the rigor of a mathematician, so what happens is you build up piles of "coincidences" until a reasonable person would be hard-pressed to believe they are only coincidence.

Hence the idea of reasonable doubt which has a specific meanings in various jurisdictions:

http://en.wikipedia.org/wiki/Reasonable_doubt

None of the items taken by themselves are enough to convict (e.g., other people would be tweeting about Silkroad 2 at the same time), but you add it all together (server in his name, piles of unexplained cash and large purchases, tweeting about it, accessing the servers from his machine, etc., etc.) and it starts to look really bad.

Plus he's also confessed, apparently.

This seems like an excellent example of a 'natural experiment' where the FBI's imaging request serves as an instrumental variable.