Fediverse

Some time ago I started following some Twitter accounts from the Mastodon instance I'm on, via one of the many Birdsitelive instances. Suddenly they all disappeared and I thought of a server down; no problem I followed them again via another Birdsitelive instance. Until this week: also those ones disappeared. Then I asked to my admins, they answered they are blocking Birdsitelive instances one by one because of their huge resource consuming on server. But: shouldn't the "weight" be on the side of the Birdsitelive server? From Mastodon I'm only reading, I shouldn't being generating anything. Am I missing some technical info?