The existing grass and particularly weeds will likely just grow through the new soil. In the case of grass, that generally isn't a huge prblem, but with weeds it is. You can get a turf cutter to sut up the top layer with the grass and weeds so you can remove it before the new soild and grass goes down.

Also check with your local lanscaping places, many of them have free or cheap disposal for landscape / green waste - but again you need to look at how you will transport it there.

(hell, if you were closer to me I would happily take those rocks off your hands! I am forever filling in holes my dogs have dug to try and get in the neighbours yard. )