What is the effect of Pip is narrating this story at a more mature phase of his life?
Pip often describes his child self as an adult would. The effect is a humorous or reminiscent tone.
The biggest hint that he is remembering is that there is a great deal of humor in his tone, even during events his child self found scary. For example, consider his meeting with the convict, Magwitch.
After each question he tilted me over a little more, so as to give me a greater sense of helplessness and danger. (chapter 1)
The adult Pip knows that he was not in danger, and actually does look back on the incident almost fondly, since Magwitch became family in a way. Therefore this scene is funny, not scary.
When Pip describes Miss Havisham’s spooky room, it is again from a reminiscent point of view.
An épergne or centre-piece of some kind was in the middle of this cloth; it was so heavily overhung with cobwebs that its form was quite undistinguishable; and, as I looked along the yellow expanse out of which I remember its seeming to grow, like a black fungus, I saw speckle-legged spiders with blotchy bodies running home to it, and running out from it, as if some circumstances of the greatest public importance had just transpired in the spider community. (chapter 11)
Pip grows and matures quite a lot during the course of the book. Although he does not directly comment on events often, his tone often is slightly reminiscent as with this example, or showing humor.