I have these concrete slabs on my patio, each about 3 feet square,
arranged in a matrix. There is a gap between the slabs 1-2 inches
wide, and weeds like to grow through the gaps like mad. There is
gravel there now, but soil has started accumulating and it's not
keeping the weeds out (this is how it was when I moved in).

What I really want to do is dig the gravel out and put something
impervious in it's place. Something like concrete would be nice, but
I don't think that's the best solution. Any suggestions? The gaps
are fairly consistent, but not perfect I'm sure. A type of liquid
rubber, or anything else that can be poured in and allowed to set
would be ideal, but I have no idea what is available.