The later Stocker & Yale military watches had this ugly seconds hand with a huge paddle on it:
I've read that the paddle acts as a counter-balance to the much longer arm with the arrow on it - but you can't really judge by just looking at it. However, it can be calculated if you know the areas of the various geometrical figures that go to make up the seconds hand's outline.
So I took a macro photo of the hand, brought it into PhotoShop and measured the needed dimensions (in pixels). Then, like a pilot checks the Weight and Balance of an aeroplane before taking off, I calculated the moments of area for each arm of the seconds hand. It's OK to use area instead of weight because the hand is made of thin sheet steel which means that, if the areas balance, so will the weights. The units end up as pixels cubed - because area was measured from the image as pixels squared and the distance of each geometrical figure from the center was also in pixels. Ordinarily, moments are given in units of force x distance - for example Newton-meters.
The paddle side came out at 1.73 Mpx3 and the arrow side came out at 3.29 Mpx3, almost twice as much. So, it's not balanced, even though it looks like it. The specification for the movement, a Ronda 715, states that the out-of-balance for the seconds hand is to be less than 0.04 μNm. So, some unbalance is allowed but, to check compliance, it would be necessary to use real units of mass instead of the above pixel-area short cut. I'll do it one day, just out of curiosity.
Best regards, xpatUSA