Should each chapter in an extensive paper start with an overview of the chapter's contents?
The last time I wrote a long paper with a multistep argument, I endowed each section (there were 15 or 16 of those and the total article length was 87 pages in the 12pt font) with the "objective statement" (In this section we show that there exists a partition of the set $E$ into "cells" with the following properties ..., etc.). Moreover, I italicized these objectives. The reasons I did it were

a) some of the sections were devoted to things that are known to experts but hardly to the "general audience", so which sections to read and which to skip would heavily depend on the reader's general background

b) If you read the italic font alone, you can see the general flow of the proof without computations or technical details. You may then concentrate on "most suspicious" or "least known" places first.

I had mixed feelings about doing so too, but it looks like the readers have liked it so far. In general, the main question you should ask yourself is whether what you do will facilitate the reading. Everything else (paper economy, stylistic beauty, etc.) is secondary. If you expect 20-50 people to read what you wrote and if you can spare each of them mere 20 minutes (the minimal time needed to verify the ubiquitous phrase "direct computations yield"), you advance the general human progress by 7-14 hours already.

Note that what I did was different from the "Chapter" approach because I put only one complete logical step into each section. Also it was not about the Lemma/Sublemma/... division, which more often than not reflects the technical convenience rather than the logical structure. Some sections contained several lemmata needed to carry out the corresponding logical step and some lemmas were done in two steps. 

The last thing I want to say is that, when reading, most people, including myself, prefer a repetition to an omission, and being over-informed to being under-informed, so few people, if any, will criticize you for being too clear or too slow.