"Very busy" doesn't mean the same thing as "busier". "Busier" is a comparative: more busy than something else. You could be busier than another person, or busier than you were yesterday, etc. "Very busy" is an absolute. It is not compared to anything. If I say that I am "very busy", that says nothing about whether I am busier than I was yesterday or not. I could be very busy today but not as busy as I was yesterday, etc.
"Too busy" is different from either of the others. "Too busy" says that I am over some threshold. Again, I could be "too busy" but still be less busy than I was yesterday. I suppose "too busy" normally implies "very busy", but not necessarily. Maybe I'm not all that busy, but I nevertheless I am too busy to do some side task.
Busy-ness is hard to quantity so it's hard to nail down these words. But consider some more absolute word, like "hot". If it was 50 degrees yesterday and 60 degrees today, than it is hotter today than it was yesterday, but few would call 60 degrees "very hot". If it was 110 yesterday and 100 today, it is surely very hot, but not hotter than yesterday. If it is 40 degrees it is too hot for ice to remain solid, but we probably wouldn't call that "very hot". Etc.