Cosimo is the Grand Duke of Florence, though he is only a child around Andrea’s age. As such, he is led mostly by his Catholic advisers, and even when he comes to an age of reason, he continues to parrot their beliefs. His age and lack of maturity can be readily seen in the physical tussle he gets into with Andrea over a wooden model of the solar system. Because Cosimo is so easily handled by his staff, it is impossible for him to assist Galileo, although it’s not clear that he would want to assist Galileo even if he could.