While reading Va'etchanan last Thursday, I notice that the weekday reading ends in the middle of an aliyah (spec. the Sheni aliyah.)
I am unaware of any minhag that ends the reading of Va'etchanan at Shlishi. That would make for a very long weekday reading, so perhaps, this was not done b/c of tircha d'tzibbur?
I viewed the parsha (meaning "paragraph" as it is written in a Torah scroll) breakup of the beginning of Va'etchanan, as we need to assure that there are at least 3 verses available to be read before a paragraph break.
There is a petucha ("open" paragraph break) after Devarim 3:28. The reading begins at 3:23. So:
Cohen could be 3:23 - 3:25 (3 verses, as it currently is) Levi could be 3:26-3:28 (3 verses and end at the par. break) Yisra'el could be 4:1 - 4 (4 verses and ending at Sheni itself)
Why didn't they stop at Sheni, seeing that it would fit the halachic requirements for both proper aliyah breakup as well as reading a minimum of 10 verses for weekday reading?
Note If there are any customs that do stop at Sheni as I have proposed, please state who does this and how the aliyot are broken. If possible, state why they do and others don't. (I daven Nusach Ashkenaz, FYI.)