[...] nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; [...]
There's quite a bit of [link|http://caselaw.lp.findlaw.com/data/constitution/amendment05/02.html#1|case law about it].
Briefly, a civil trial and a criminal trial are completely different even if they are both based on a common event. Similarly, a federal trial is completely different from a state trial. Under our system, Blake wasn't under double jeopardy because the charges weren't the same.
I agree with you, to some extent, that it does seem like a way to punish a person who was found not guilty. I'm not sure there's a good way around that though.
Cheers,
Scott.