The balloon will be filled by a gas, and as the gas is not escaping we can assume that it is at a constant pressure.
The KMT (Kinetic Molecular Theory) explains the macroscopic properties of gases. This theory states that gases are formed by particles in constant motion, and that their kinetic energy is directly proportional to the temperature of the gas.
If we leave the balloon filled with gas in the sun we assume that the temperature of the gas inside will start to rise. When the temperature starst to rise, and the pressure is constant, particles will gain kinetic energy. This will result in particles moving faster and coliding with each other and with the balloon's walls more often. As a consecuence the particles will tend to stay farther from one another and the volume of the balloon will increase.
This is an example of Charles's Law that states that at constant pressure the volume of a gas is directly proportional to its temperature. In other words, when the temperature of the gas increases the volume increases as well.
To summarize, if we fill a balloon and we leave it in the sun its volume will increase.