The 'branches' are emergent macroscopic phenomena. They are also arbitrary to a degree. You can choose to threat the entire section of the multiverse where the cat is dead as a single branch. Or you can split it in many branches where the cat is dead in many different ways. Of course the 'thickness' of these branches would be different. The trouble is as you go down the path of splitting branches they become less macroscopic and more fuzzy at the edges until they disappear entirely. So yes, counting them accurately is a challenge.
And to answer the question,yes, some branches will count more than the others even though all of them are real. I understand 'equally real' to mean that a particular branch does not become 'more real' simply because I just happen to be in it. For example, I might personally witness a quantum experiment to produce an outcome which is, according to all computations, extremely unlikely. This outcome is of course as real as it gets because I just saw it happening but it is still in some sense 'less real' than the other more likely outcome.
This is in contrast with a) objective collapse where the unobserved branches are constantly cut off and thrown away without a trace or b) Bohmian mechanics where the pilot wave completely describes the entire multiverse but particle trajectories select one true 'real' path through it or c)various consciousness-causes-collapse theories where everything I see is real and everything else is a figment of my imagination.