Weight is meaningless in space because you have to have a reference force vector as a point of comparison - your weight near a black hole will be considerably higher (by several orders of magnitude) than your weight on earth, and the weight of your feet will be far greater than the weight of your head (usually leading to rapid spaghetification).
You can talk about density, which is an indication of the mass of a particle per unit area. Density of particles in the solar system is fairly high - hundreds of atoms per cubic centimeter, mostly due to the stellar wind. In interstellar space, that number drops to perhaps 10s of atoms per cubit meter. In intergalactic space, the number is probably only one or two atoms per cubic kilometer. When you get to the voids, it's conjectured that you may be looking at handfuls of particles per light year. The voids are very, very empty.
However, even that's not a clean answer, because space itself has vacuum energy - because Planck's constant is not quite zero, there is a small probability that at any given point a particle may be brought into existence due to the energy of the vacuum. Thus, while the density of an arbitrary region in space may be close to zero, it will never be at zeron.