 All the beans were under the same conditions.  The smallest beans grew sprouts of 25cm.  The middle sized beans grew sprouts of 12cm  The large beans did not grow at all.  The middle sized beans admittedly grew as expected.

 Different sized beans need different amount of resources in order to germinate.

We developed this theory BECAUSE :  The bigger beans are more in competition with each other because they are bigger and so require more resources, however all the beans are under the same condition of moisture, air and temperature.

On the basis of:  The evidence of the experiment.  The knowledge that the conditions required for germination of seeds are heat, moisture and air.  Observation of life in general, for instance small babies need a lot less food during the day than a fully grown adult.

 Because we assume there is plenty of air and the temperature sufficient for growth, surely the main issue is the competition for water among the beans. All the beans were given the same amount of water and the smaller and middle ones grew but also with different results with the smaller ones growing larger.

We believe our theory is a valid explanation....UNLESS:  they are different species of bean which need different conditions for germination.  Different sized beans were differently treated before entering the shops/were bought.  The bean plants where the big beans came from plants that were affected by some disease and so the beans are dead.  Perhaps they are genetically modified beans.