I heard that some still have a custom to boil only odd numbers of eggs at a time. I heard that the reason is if there is a blood-spot in an egg, the egg will be Battel Berov. This only explains why people don't boil one or two eggs at a time. What is the issue boiling 4 or more eggs at a time?
If you find a blood spot in a hard boiled egg does that affect the other eggs boiled with it in the pot?
If there were 3 or more eggs cooked with it in the pot then there is no problem with the other eggs [because of the concept of 'batleh b'rov' (nullified in the majority)]. If there were exactly 2 eggs then it depends: If you hold the lenient view stated above then the 2nd egg is unaffected. If you hold the stringent view stated above then the 2nd egg must be discarded since there is no batleh b'rov here.
It sounds to me like an halachic ex-post-facto rationalization of a superstitious practice -- see comments above and other answers. It is actually quite common to see rabbinic explanations of what are ultimately traceable to superstitious non-Jewish peasant beliefs. (As a random example off the top of my head, R' Menashe Klein's explanation of children throwing a tooth into a mouse-hole and saying "mouse, mouse, I am giving you an old tooth, give me a new one in its stead", explained as halachic concerns for burial of the tooth, where it is really traceable to a pagan custom.)
I would point out the following two opposing considerations:
1) There is an existing superstitious practice in the non-Jewish world to prefer an odd number of eggs. This is in terms of placing eggs under a hen or goose to hatch. This preference for odd numbers extends at least to Virgil. It thus stands to reason that this is an extension of the superstition to the boiling of the eggs, and one should avoid engaging in such superstitious behavior.
2) Even if the issue truly is odd vs. even for superstitious/demonic concerns, Chazal themselves adopted (in Bavel; in Eretz Yisrael they discarded it) the concern for zugos.
I have always heard that the reason for specifically always having an odd number is because we don't want to have Zugos - pairs.
[No source. Just what I've heard.]