In addition to that the vehicle is extremely weak when lying on its side. I should think there's a good chance the tanks could be damaged by waves bending the vehicle.

Correct. Also the terminal velocity even with a parachute can be high, and if you hit a rising wave, even more.

Actually parachuting and fishing the stage from the sea was their first idea, but they never recovered a single stage that way, and moved to active controlled recovery, which is much much much better in my opinion.

Estimates I've heard say 15% loss of payload mass for a barge landing, 30% for land.

What do you mean by "loss of payload mass"? If the rocket lands on a barge it has to reduce it's payload by 15%?

Any ideas why it's higher on land? Seems like it wouldn't differ that much.

Ascent trajectory is much different. Orbit is mostly about horizontal velocity, the altitude is just to get above the atmosphere and is the easy part. For the first stage to return to its launch site for landing, it has to cancel out all of the horizontal velocity it builds up while lifting the second stage and payload, then turn around and come back. A barge landing can use a more optimal ascent trajectory and have the first stage land several hundred kilometers away from the launch site.

You have to accelerate the rocket back to the launchpad if you want to land on solid ground -- there's no convenient landmasses at the right distance. That takes fuel.

I assume the rocket is in geosynchronous orbit? Otherwise it would just be a timing issue (i.e. fire the rockets when you're over land).

The booster never reaches orbit as it is on a ballistic trajectory