A note on this statement is included by Stillman Drake in his Galileo at Work, His Scientific Biography (1981): Galileo adhered to this position in his Dialogue at least as to the "integral bodies of the universe." by which he meant stars and planets, here called "parts of the universe." But he did not attempt to explain the planetary motions on any mechanical basis, nor does this argument from "best arrangement" have any bearing on inertial motion, which to Galileo was indifference to motion and rest and not a tendency to move, either circularly or straight. 
Letter to Francesco Ingoli (1624)
                                    
“Whence do you have it that the terrestrial globe is so heavy? For my part, either I do not know what heaviness is, or the terrestrial globe is neither heavy nor light, as likewise all other globes of the universe. Heaviness to me (and I believe to Nature) is that innate tendency by which a body resists being moved from its natural place and by which, when forcibly removed therefrom, it spontaneously returns there. Thus a bucketful of water raised on high and set free, returns to the sea; but who will say that the same water remains heavy in the sea, when being set free there, does not move?”
Letter to Francesco Ingoli (1624)
Help us to complete the source, original and additional information
Galileo Galilei 70
Italian mathematician, physicist, philosopher and astronomer 1564–1642Related quotes
                                        
                                        Journal entry (2 March 1861), Ch. 5 : The Beginning of the War. 
Lucy Larcom : Life, Letters, and Diary (1895) 
Context: What does cause depression of spirits? Heavy head and heavy heart, and no sufficient reason for either, that I know of. I am out of doors every day, and have nothing unusual to trouble me; yet every interval of thought is clouded; there is no rebound, no rejoicing as it is my nature to rejoice, and as all things teach me to do. We are strange phenomena to ourselves, when we will stop to gaze at ourselves; but that I do not believe in; there are pleasanter subjects, and self is a mere speck on the great horizon of life.
                                    
Microcosmos: a Little Description of the Great World (1621)
                                
                                    “My arms are killing me.
I didn't know words could be so heavy.”
                                
                                
                                
                                
                            
Source: I Am the Messenger
“What uniform can I wear to hide my heavy heart? It is too heavy. It will always show.”
Source: The Holy Terrors