I do believe Galileo's belief in heliocentrism was brave at the time. In 1615 the Roman Inquisition investigated his findings and found them to be false of all things. He was opposed on all sides and his book containing the findings was banned. If that's not brave, I don't know what is.
The reaction at the time is important. How we view Galileo today is important too. We can either say that clearly Science trumps religion, but the religious of that day were bufoons, monkeys, idiots. To say that the religious today are idiots is not true, because Science and religion are melding in ways.
I personally think that Galileo's belief in heliocentrism was brave at the time because of his scientific ideas as well as thoughts that got him to sharing what he wanted. I personally think that Galileo's belief had people wondering how he came up with thoughts that led up to science.
Galileo was persecuted for his beliefs, almost being put to death during an inquisition period and only saved by the direct intervention of the Pope at the time, who was a sort of fan and who talked with him extensively. Galileo was a visionary, and his views were not accepted by society at the time.
Yes, I think that Galileo's belief in heliocentrism was brave at the time, because he got a lot of backlash for his beliefs. Galileo's beliefs and scientific positions were condemned by the community, including the Christian Church. Galileo needed a lot of bravery to continue with his work in the face of criticism and controversy.
It is logical to assume that he was aware of the consequences, in which often included death. Consequences in which fell pain him were quite great for such theories, in addition to his own scientific theories. Despite his inevitable punishments, I'd like to assume that he lacked regrets (with the exception of possibly concealing his identity; that could have been a good idea).