OK, there are viruses with multi layered capsid. Fun fact, these are mostly harmless for humans, but can be harmful for cancer , .
The idea you want, striking twice, has little to no evolutionary sense. Here you have it "by the numbers":
Virus only attack to reproduce.
Killed human does not help them to reproduce.
Strong humans with a lot of strong, well fed cells are best to reproduce.
Only thing virus "want" weak is immunological system.
There is literally no need for virus to kill someone after virus reproduced. Actually, it is worse because host will no longer spread the virus. Most succesful viruses are ones that let their victims spread viruses for quite long time.
The only kind of viruses that kill humans are the ones that, simply, reproduce too fast and overwhelm our systems. But many of them, like pig flu, also "feed" on animals, on which they have less lethal effects.
Natural evolution seems difficult *, for above reasons. But given that there actually are multi-layer viruses, I see no particular reason against something like this as bio-weapon. With weapon, there is actual reason for it to kill, so outer layer as reproduction and inner layer to kill starts to make sense.
* Will's answer shows I may be wrong here.