Eating eggs and cheese to refute heresy?
Hard to truly understand what Zosima is trying to say, but in general the Orthodox Churches has a far stricter set of rules when it comes to fasting than the Western Churches.
For example in the Catholic Church butter, eggs, cheese are common fare on fasting days, but in the Orthodox Churches these are not eaten on fast days. The Orthodox are still holding on to their traditions and basically that is very commendable.
The West has stopped abstaining from these foods Holy Week, but the East has retained them.
The idea of abstaining from these foods at different times of the year is simply because they are considered animal based products.
At one time in Christendom, almost all practiced fast very seriously, but now it seems that the Orthodox are the main forerunners in keeping this tradition alive.
It is most noble to say the least, but in this domain they stick out as holding on to tradition very firmly.
This may be the sense that Zosima is speaking of, in keeping the Orthodox Faith free from following the West and possibly their heresies.
Without any more details one cannot make an absolute decision.
One point, I do not understand is why he would choice Cheesefare Week and Bright Week for fasting?
Bright Week is a time of genuine religious celebration!
Bright Week or Renewal Week is the first week following the Resurrection of Our Lord and Savior Jesus Christ, which is celebrated each year at Pascha. It ends the following Sunday, the Sunday of St. Thomas. For Orthodox Christians Bright Week begins a period of celebration that continues for fifty days until Pentecost.
This celebration includes the practice of the faithful joyously greeting each other with the salutation of Christ is risen, followed by the response indeed He is risen or truly He is risen, as the whole of creation is renewed by Our Lord and Savior. The services of Bright Week are done with the Royal Doors fully open. This unblocked view of the altar symbolizes the open door of Christ's empty tomb as well as the rent veil of the Jewish Temple, which was torn apart at the moment Christ died.
The entire week is considered to be one continuous day and the main reason why fasting is completely prohibited to all Orthodox during the week.
As for Cheesefare Week, it is a sort of a very modest form of feasting just before the Great Lent. It brings back the thought of Pancake week here in the West.
Cheesefare Week, also known as Maslenitsa (Ма́сленица), Butter Week, or Pancake week. It is celebrated during the last week before Great Lent—that is, the seventh week before Pascha (Easter). Cheesefare roughly corresponds to the Western Christian Carnival (Mardi Gras, or Shrove Tuesday), except that Orthodox Lent begins on a Monday instead of a Wednesday, and the Orthodox date of Easter can differ greatly from the Western Christian date. In 2008, Cheesefare was celebrated from March 2 to March 8.
Cheesefare is the last week before the onset of Great Lent. During Cheesefare week, meat is already forbidden to Orthodox Christians, making it a "meat-fast week" (Russian myasopustnaya nedelya (мясопустная неделя)). During Lent, meat, fish, dairy products and eggs are forbidden. Furthermore, Lent also excludes parties, secular music, dancing and other distractions from the spiritual life. Thus, Cheesefare represents the last chance to partake of dairy products and those social activities that are not appropriate during the more prayerful, sober and introspective Lenten season.
It seems ironic that many Christians now feast just before Lent. In the Roman Catholic Church fasting was gradually introduced liturgically just prior to Lent with the Season of Septuagesima
The Syriac Orthodox still practices the Fast of Nineveh, a three-day fast starting the third Monday before Clean Monday from Sunday Midnight to Wednesday noon during which participants abstain from all dairy foods and meat products. However, some parishioners abstain from food and drink altogether from Sunday midnight to Wednesday after Holy Qurbono, which is celebrated before noon.
In Syriac Christianity, the Fast of Nineveh is a three-day fast starting the third Monday before Clean Monday from Sunday Midnight to Wednesday noon during which participants abstain from all dairy foods and meat products. However, some parishioners abstain from food and drink altogether from Sunday midnight to Wednesday after Holy Qurbono, which is celebrated before noon. The three day fast of Nineveh commemorates the three days that Prophet Jonah spent inside the belly of the Great Fish and the subsequent fast and repentance of the Ninevites at the warning message of the prophet Jonah according to the bible. (Book of Jonah in the Bible). Marutha of Tikrit is known to have imposed the Fast of Nineveh, and served as Maphrian of the Syriac Orthodox Church until his death on 2 May 649.
The whole idea of Mardi Gras seems foreign in the minds of traditionally minded Christians.
Is Zosima referring to Maslenitsa, the last week before Great Lent? It does make sense, but without knowing what he meant, one is unable to really know. This may be the reason why he abstain from certain foods during Cheesefare Week?
Maslenitsa also known as Butter Lady, Butter Week, Crepe week, or Cheesefare Week) is an Eastern Slavic religious and folk holiday, which has retained a number of elements of Slavic mythology in its ritual, celebrated during the last week before Great Lent, that is, the eighth week before Eastern Orthodox Pascha.
The date of Maslenitsa changes every year depending on the date of the celebration of Easter. It corresponds to the Western Christian Carnival, except that Orthodox Lent begins on a Monday instead of a Wednesday, and the Orthodox date of Easter can differ greatly from the Western Christian date.
The traditional attributes of the Maslenitsa celebration are the scarecrow of Maslenitsa, sleigh rides, festivities. Russians bake pancakes and tortillas, Belarusians and Ukrainians bake dumplings, cheese cakes.
As for his abstaining during Bright Week, that may be a little harder to flesh out.
There is at least one of the Church Fathers that states if we over indulge in eating after a fast, we may lose all the merit we might have gained during a fast, such as during the Great Lent. Unfortunately, I can not remember who made this point, but will add it when I find it.