Is there any relationship between the voltage and the physical size of the battery?

No. Voltage is mainly correlated with the types of metals used to produce the battery. For example, many common batteries are made of NiZn (Nickel and Zinc), the combination of these metals transferring electrons through an electrolyte produces approximately 1.5V - 1.65V (volts).

Many batteries are made of these metals, therefore they will all give off the same voltage. AA, AAA, C, and D batteries all give off 1.5V (if they are made with NiZn). The size difference accounts longer battery life, or even spreading the batteries current out over a greater distance.

Now the 9 volt battery is a little bit different. In the common AA battery, there is a typically a Zinc rod, surrounded by a paste (the electrolyte, or a bridge for the electrons), the paste is contained within a Nickel tube (lets call this tube/paste/rod mixture a "cell"). Electrons are passed from the metal to metal creating an electric current that produces 1.5V. But What would happen if you took one of these cells, and connected it to another identical cell? The resulting voltage would be 3V. What the 9 volt battery does, is it takes 6 NiZn cells and connects them together, thus producing 9V.