Dumbledore began to tell Sirius everything Barty Crouch had said. Harry was only half listening. So tired every bone in his body was aching, he wanted nothing more than to sit here, undisturbed, for hours and hours, until he fell asleep and didn't have to think or feel anymore.
There was a soft rush of wings. Fawkes the phoenix had left his perch, flown across the office, and landed on Harry's knee.
“'Lo, Fawkes,” said Harry quietly. He stroked the phoenix's beautiful scarlet-and-gold plumage. Fawkes blinked peacefully up at him. There was something comforting about his warm weight.
Dumbledore stopped talking. He sat down opposite Harry, behind his desk. He was looking at Harry, who avoided his eyes. Dumbledore was going to question him. He was going to make Harry relive everything.
Harry Potter and the Goblet of Fire
I don't know what "his warm weight" refers to here. Is it Harry's weight or something? What does it truly mean?