How is this burden less for members on “Daily Digest” than for thoseThe total size of data communicated may not be that much different.
But the total burden is likely less for Digest because there would be up to 12 messages represented in a single digest. So that's up to one twelfth the number of transactions between Groups.io's mail server and the member's. Each of those transactions include overhead in both processing and communication.
If we define these as “incoming”, wouldn’t the messages I sendWe've got our terms reversed: I was speaking from Groups.io's point of view. That is, when you post a message that is "incoming" to the group, and when it is sent out to the members that is "outgoing" from the group. Nevermind that though (the point of view is arbitrary).
A message you send to the group does consume some resources, at FatCow and at Groups.io, but then Groups.io's resource consumption when the message is sent to the group members is multiplied by the number of members - several hundred times over in your example groups. That multiplication effect doesn't affect FatCow, except to the extent that your group has more than one member using FatCow (and then the multiplier is only the number of those members).