The best tip I've gotten for quilting in a standard sewing machine (which I do in my little Elna which only has a 6.5" throat) was to have a chair or small table next to the the end of your sewing table. This will help take the weight off.
Also don't Pull the quilt, help guide and feed it through (your muscles with swear your doing more than that but what do they know?). I'm certain you're on the right track here, I have done a Queen quilt in my little machine and didn't hesitate for a moment to start a king. You can try making your stitch length a bit shorter. This will amount to smaller stitches all over, for the most part the stitch in the ditch stitches sink into the quilt and can hardly be seen anyway.
Relax you can do this. If your sewing machine has an adjustable pressure foot you might try adding more pressure to help with the pull, but if not don't worry about it. My little Elna doesn't have that feature and works fine without it, but my Brother machine has it and does need adjusted depending on the project.
If it is the weight you can sort of feel the quilt pull a little bit off the edge of the machine. If that's what is happening adjust the quilt a bit until the pull/drag feeling is a bit less.