After reading pages 143 and 144 many times, and analyzing what the hat that Rezia is sewing for Mrs. Peters, I have come to think that this passage is representative of Septimus's life, from when he returns from the war to his death. I may be totally wrong, but I think the hat is representative of something much bigger.

"He began putting odd colours together- for though he had no fingers, could not even do up a parcel, he had a wonderful eye, and often he was right, sometimes absurd, of course, but sometimes wonderfully right"
In this passage, Septimus's perception is brought up. His absence of fingers suggest that he is a different person after coming back from the war; however, he has a "wonderful eye". In the eyes of society, he is absurd, but Septimus is actually wonderful, and contrary to what Holmes and Bradshaw and the rest of society believe, he is "right" according to Woolf.

"'She shall have a beautiful hat!' he mumured, taking up this and that, Rezia kneeling by his side, looking over his shoulder. Now it was finished- that is to say the design; she must stitch it together. But she must be very, very careful, he said, to keep it just as he had made it."
Although Septimus is capable of seeing "wonderful things", he needs Rezia to support him and help him "stich" his fragmented perception together. He depends on her to help him see what society sees and ultimately give him life.

"So she sewed.... The sun might go in and out, on the tassels, on the wallpaper, but he would wait, he thought, stretching out his feet, looking at his ringed sock at the end of the sofa"
"It was wonderful. Never had he done anything which made him feel so proud. It was so real, it was so substantial, Mrs. Peters' hat."
The sewing of the hat relates to Septimus's life. The inward and outward pattern of sewing is yet another reference to the up and down, wavelike nature of life. Rezia sews and sews, up and down, until the last stitch is complete. This resembles the end of life. The final downward stitch is similar to Septimus's final downward motion- his jumping out of the window. By describing the final product as "wonderful" and "substantial", Woolf reveals the inevitable nature of death. She also demonstrates Septimus's attitude towards death. He feels "proud" to have finished something that in his mind is beautiful, and similarly feels defiance when ending his life, which only he and Rezia perceive as "wonderful".