During a regular (non-leap) Jewish year, there are four instances where two of the weekly Torah portions are read together in the same week. This is because there are not enough weeks to read all of the portions separately (especially because we do not read a weekly portion during Shabbos of Pesach and Sukkos). Why were those eight specific portions chosen for doubling?
The Parshoyos that are sometimes doubled are: Vayakhel-Pekudei, Tazria-Metzora, Acharei-Kedoshim, Behar-Bechukosai, Chukas-Balak, Matos-Masai, Nitzovim-Vayelech.
The Gemara in Megila 31b says that Ezra established that the curses of Chumash Vayikra should be read before Shavuos and the curses of Chumash Devarim should be read prior to Rosh Hashana.
The Rambam in Tefila 13:2 mentions that the Minhag is to read Bamidbar before Shavuos, Veschannan after Tisha B'Av, Nitzavim before Rosh Hashana, and on a year with one Adar - Tzav before Pesach.
Although there may be other reasons - it seems that the Parshios selected are more connected in content than the others.
I am expanding on Gershon's answer so that you can see things more clearly.
The Gemarah Megillah dictates a large part of the calendar on its own. Here's how:
"the curses of Chumash Vayikra should be read before Shavuos"
This explains why there is a "burst" of doubled portions between Pesach and Shavuot during a non-leap year. Three of four weeks during Sefira are doubled portions. If the last day of Pesach occurs on Shabbat in Diaspora, in a non-leap year, Behar-Behukotai is separated in Israel. (I have stated this in "reverse" intentionally, b/c usually in a non-leap year, we expect these two to be doubled everywhere. However, in this scenario, Israel is 1 week ahead of Diaspora.)
V'eschannan after Tisha B'Av
This is mentioned by Ramba"m, and I have to see if he or a commentary mentions a reason as to why this is important, as it' snot mentioned in the Gemarra. Doing this explains why Matot and Mas'ei are almost always doubled. There are a few rare exceptions when they are separate. Separation occurs only in a leap year when Pesach occurred on Sunday or it is a maleh leap year with Pesach being on Tuesday. In Israel, it can also occur when Pesach started on Shabbat, as you will see next year (5779).
the curses of Chumash Devarim should be read prior to Rosh Hashana
Interestingly enough, this rule is "superseded" by Rambam's
Nitzavim before Rosh Hashana
because Ki Tavo is always read two weeks before Rosh Hashanna; never immediately before. (I don't know why.)
Netzavim is paired with Vayelech when either Rosh Hashanna or Yom Kippur occur on Shabbat. This is easy to understand why. When neither occur on Shabbat, as in this year, there is an extra SHabbat between Yom Kippur and Succot available to read Ha'azinu, otherwise, Ha'azinu is read on Shabbat Shuva.
(Vayelech has the anomaly of being read either 0, 1 or 2 times within the same Hebrew year.)
As for why those specific parshiot were chosen for doubling, Gershon is correct that they tend to have similar content. But, that is part of the story. This lengthy article explains that much of the doubling has to do with parsha "size management". As a Torah reader, after I read this article, I walked away still shaking my head wondering about how well they really "managed" this. Matot / Mas'ei is a 4-water-bottle-sipping double!