The Nikon 1 system is based around the Nikon CX sensor size (1"-type), which has a mean crop factor - 2.7x in relation to Nikon FX, 1.8x in relation to Nikon DX. If the lens you want to hold on to gives a wide field of view on your DSLR, it will probably give a standard or even short telephoto field of view on a Nikon 1 camera.
If you're currently using an entry-level Nikon DSLR (D3000- or D5000-series), the bulk you're tired of is not really from the camera, but the lenses. Using a bulky lens on a tiny camera is still a bulky setup.
If the DSLR kit is really getting too bulky for you, I'd say move on and choose a different system altogether. Sell your entire lens collection, and start from scratch. Full-frame mirrorless (Sony Alpha 7 series) won't really give you anything in terms of weight savings, and APS-C mirrorless systems (Fujifilm X, Sony a**00 / NEX, Samsung NX) will be significant mostly with prime lenses. If you want smaller and lighter, while still using semi-fast zooms, Micro Four Thirds is probably the best choice.