The concept of balance is less subjective than you think, unless you consider all perceptions subjective! :)
Here's how to develop an eye for it: browse around your local area and/or Flickr, Google images, or any other source of photographs of the real world and look at photographs of objects that are clearly balanced (stable) and unbalanced (ready to fall over or tilt unless supported).
Our perception of balance is grooved in by our experience with physical objects, starting with those blocks you probably played with when you were 2 years old. We see balance based on our experience of the physical world. Picture a set of scales with a 3 kg weight on one pan and a feather on the other. You perceive that as unbalanced because in the real world it would be.
It is this experience that translates into design, where gravity plays no actual physical role. In your example, if those were metal objects held together by a frame, the center of gravity would be to one side; it would fall over.
Once you've got this under your belt, experiment with some shapes cut out of paper. Play with their arrangement and notice which feel balanced and which don't.
A perfectly balanced layout isn't always what you want. Balance is at rest, in equilibrium, static. More often than not, you will want to add some tension or energy to a layout. That is achieved by carefully unbalancing the elements to achieve the effect you want.