Why do Cheshvan and Kislev vary in length?

Question

In general, Jewish-calendar months alternate in length: odd-numbered months have thirty days each and even-numbered months have twenty-nine. However, it is sometimes necessary for a year to have one fewer or one more day than would thus be allowed, so a day is added or removed from the calendar. Specifically, in nearly half the years, Marcheshvan, though the eighth month, has thirty days; in half the remaining years, Kislev, though the ninth month, has but twenty-nine days.

Why were Marcheshvan and Kislev, specifically and rather than any other months, chosen to vary in length?

Answer 1

Rambam Le'am (Mosad Harav Kook, 5717) to Hilchos Kidush Hachodesh 8:6 explains that we want to make all required adjustments at the first possible opportunity in the year. We do not want to do anything to affect Tishrei because of all the Yomim Tovim in that month, and so the next possible months which we can change are Cheshvan and Kislev. (See also "Na'veh Kodesh" to Rambam there, who brings the first half of this explanation).