You probably already know this, but the plumb bob points to the spot inside the wing where the center of gravity resides.  If you want it to point to the spot outside the wing where the center of gravity is located fore and aft, then you need to have the plane level (think about it).

Moreover, if you make a harness by tying all your strings to a point, then you can measure the side-to-side CG (which, on a CL plane, should be outboard of the center thanks to tip weight).

The CG isn't just somewhere between the leading and trailing edges -- in the case of the plane you show, it is inside the wing.  In something like a Piper Cub, it's below the wing; in a low-wing plane like an Ercoupe or a P-51 it'll be above the wing.

Maybe this drawing makes it clear.  The pointer always points to the CG, but you've moved the wing around the CG by changing the tilt of the aircraft.

That thing should be great for determining the CG.  I should build one myself!

Mike's gizmo is what I was talking about when I mentioned tying all your strings at one point.

Might be a good point in time for a technical explanation of each by one of the engineering guys here.

Ouch.  I tried.  I gave up.  I understand what "center of gravity" means, but I'm having trouble trying to describe it in a way that's less confusing than Wikipedia.

So, here's what Wikipedia says: http://en.wikipedia.org/wiki/Center_of_mass.  I have a nasty suspicion that it'll be perfectly clear if you already know what it's talking about, and as clear as mud if you don't.  I sincerely hope that I'm wrong.

One thing I will say, that may be of help: the center of gravity (or the center of mass) of a rigid object is a fixed point associated with the object.  It is often inside of the object (in the case of a conventional stunt plane, it should be centered vertically in the wing, much closer to the leading edge than the trailing edge, and somewhat to the outside of the circle than the center of the fuselage, to balance the lines).  When you stick weights onto the nose or tail of a plane, you're adjusting the longitudinal location of the center of gravity; when you put weights into (or take weights out of) the weight box on the outboard wing, you are adjusting the side-to-side location of the center of gravity.

So usually when you hear someone talking about "the center of gravity" they're really talking about the longitudinal balance point.  When you hear someone talking about "the vertical center of gravity" they really ought to be saying "the vertical balance point" or "the vertical location of the (one) center of gravity".

So, I hope this helps.  I balked on writing up something about CG when I realized that to do it right I needed to run out to the shop to make some visual aids, and then take pictures or even movies.  If enough people ask, I may go do it anyway.