If nothing weighs something then doesn't that mean there is mass associated with spacetime? Lawrence M. Krauss says, "If you removed all of the particles, all of the radiation,absolutely everything from space and all that remained was nothing that nothing would weigh something." 
What weighs something has mass. If you remove everything else then all that is left is spacetime. Meaning, there is mass associated with spacetime.
Mass physically occupies three dimensional space. A particle moving through the mass associated with spacetime would displace the mass analogous to the bow wave of a boat.
If mass is associated with spacetime then wouldn't it be the mass associated with spacetime which waves in a double slit experiment?
 A: OK, I watched the video. 
It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space.
He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles all the time, and illustrates it with the proton. His discourse assumes that the proton is made up of three quarks and the rest is empty space. The theory I know does not say so, it says the rest is a gluon to quark antiquark and back sea, that holds everything together to form the proton. It is not empty space because energy exists within the proton, it is not zero.
So the presentation is incomplete and seems to me misleading, if we are to project the inside energy momentum conditions of a proton to cosmological scales and the cosmological constant. They are not the same.
Anyway the argument he seems to be leading to is incomplete.

If mass is associated with spacetime then wouldn't it be the mass associated with spacetime which waves in a double slit experiment?

In the double slit experiments, mass does not wave. The elementary particles are point particles as far as our experiments have explored, when they appear as particles, the appear at a specific (x,y,z,t). What "waves" is the probability of finding that particle at a specific (x,y,z,t) which probability  is calculated by squaring the quantum mechanical amplitude describing the "particle/wave" entity which probability shows interference patterns in collective observations at double slit experiments. 
In my opinion, until we have a solid theory which quantizes gravity and includes the standard model of particle physics speculation about how fields appear in cosmological terms is not productive. We have to wait for a theory, and a string theory seems to be the only candidate that can do this , to examine the cosmological constant of classical general relativity.
A: What I think you're trying to get at is the vaccum energy. Weight is always associated with a force, so on earth we feel the force of gravity on our body and we call that our weight. Now Einstein showed us that there is an equivalence between mass and energy. What we know from Quantum Field Theory is that there is some underlying amount of energy just sitting there at every point in the universe. But because we know from Einstein that energy and mass are two sides of the same coin, it's not wrong to say there's some amount of mass at every point in space, or that empty space 'weighs something' as Krauss liked to put it because most of us naturally associate an objects mass with it's weight from our experiences on earth.
I think your double slit idea needs a little more thought before we can get to that, but so far nobody really knows exactly what causes quantum weirdness. Some people don't even like that others ask that question.
A: https://www.youtube.com/watch?v=_rJOSDgDG0A
I think this video has a better explanation to what we're trying to get to. It is a plausible theory though. Even if we block all the radiation and remove all the subatomic particle, even then space is filled with quantum fields. And according to the heisenberg principle these fields never stop oscillating, even without any particles to set off the fluctuations. And according to Einstein, E=MC^2. Therefore empty space has some mass. (Every cubic metre of space has energy equivalent to that of the mass of 4 protons)
A: Here we are, talking about "nothing", as if it existed.  We are saying, "nothing exists", but what does that mean?  "Nothing exists", as simple as the statement may appear, yields two equal but opposite meanings.  Meaning One is that "nothing" does in fact have a state or condition of existence; Meaning Two is that there is no state or condition of pure and total nothingness.  Which is it?  The statement "nothing exists" constitutes a paradox moving around and around itself, i.e., a circular motion.  Now we have a new issue:  does thinking about this issue constitute the application of a force either accelerating the motion (Newton's 2nd Law) or at the very least, initiating the motion? Does an equal and opposite reaction (Newton's 3rd law) then come into play as a reaction force which is perceivable as weight or as weight increase (perhaps from nothing to something)?
