I'm a little surprised at how small (narrow) the barrel is. I did just a little (REAL little) bit of precision shooting in college, and the target rifles had huge barrels even for tiny .22 rounds, mostly for precision and stability.
Does it include active stabilizers? That could get rid of shake.
For the target rifles I was shooting (which have the same accuracy requirements for a sniper rifle, but not so concerned with portability), the weight was primarily to make the gun stable. Of course, that's because you're holding the rifle, not leaning against a bi-pod or other support. Then, some of that mass is absorbing recoil, which your SciFi weapon probably solves in other ways.
Of course, even with current technology, there have been so many different advances recently that it would be hard for me to compare without a huge amount of research. Extrapolate that out to SciFi, and you can have all kinds of fun dreaming up exotic materials. But in the end, you're still slinging a little bit of mass down a tube and hoping it hits where you pointed it.