Gooey build up on sandpaper when sanding
Wood won't clog sandpaper that fast, so it has to be the finish, dirt/soil or a combination of both. Paint thinner or mineral spirits usually work well to get dirt and grease off of wood, and wont harm most finishes you want to put overtop.

60 grit on a table top is a very coarse grit, and I would pretty much never use a grit that coarse on an already smooth surface. It will take a long time to get those marks out with progressively smoother grits. 

It sounds like its the finish or a combination of dirt and finish thats clogging your sandpaper.

You may want to consider using a paint/finish stripper to get down to the bare wood, then start with maybe a 120 or 150 grit and go up from there.