Then in the third aliya there is a drastic shift to a second category of mitzvot. In this category we find mitzvot which demand that we treat orphans and widows especially well, that we must look out for the needy, and that our courts must go out of their way to protect the accused. This category can be labelled as mitzvot which hold us to a high moral standard.  

Finally in category three, in the middle of the fifth aliya, we find 

mitzvot bein adam leMakom - purely between us and Hashem, such as Shabbat and the chagim. In fact there is a masterful transition between categories two and three where the Torah first describes the shemitah year, in which we work our fields for six years and leave them ownerless in year seven, with a special emphasis on how this supports the poor. Then the Torah juxtaposes it to Shabbos, which gives us six days of work and a seventh of rest but, unlike shemitah, is purely bein adam leMakom. 

Perhaps in this light we can suggest that this progression of mitzvot is teaching us a crucial message of the entire yetziat mitrayim narrative. Bnei Yisrael were learning that the G-d which took them out of Egypt was not only a G-d of justice, a G-d who punishes the wicked oppressors, a universal G-d, but that this G-d was also a G-d with a special relationship with Bnei Yisrael and a special mission and vision for them, dating back to an ancient covenant made with their great-grandfather Avraham. As the Rav explains, at Matan Torah, Bnei Yisrael were expanding their understanding of Hashem from universal to specific, from

cosmic to covenantal. (See Rashi in Yitro on "Anochi Hashem E-lokecha ")

Thus the progression of the mitzvot in our parsha has the same learning objective for us: To first understand Hashem as a universal G-d, a G-d of judgment and din, with the civil mitzvot of category one; then, knowing the G-d with high moral expectations for us in category two; and culminating with our unique relationship with Hashem, as expressed through the mitzvot bein adam leMakom in category three. 

We are a nation with a unique relationship with Hashem, and He has a special vision for us to be a Mamlechet Kohanim - a kingdom of priests who live by His high moral standards as a message to all of humanity, a mission beyond the code of law itself.  Perhaps this is why our parsha   culminates in a brit   - a covenant. Bnei Yisrael   sign, renew, and accept the brit made with Avraham Avinu  and commit to upholding it, becoming part of a glorious vision for humanity.