Which of galileo's observations most strongly supported a heliocentric cosmology? the phases of venus?

The answer is the phases of Venus. It was Galileo's interpretations of Venus that showed the theory. Using his telescope, Galileo found that Venus went through stages, just like our Moon. But, the nature of these stages could only be clarified by Venus going around the Sun. Galileo decided that Venus must travel around the Sun, transitory at times after and outside it, reasonably than rotating directly around the Earth.