Kerson Huang statements about Bose-Einstein condensation

On the Kerson Huang statistical mechanics book I read, about the Bose Einstein condensate, that for temperatures higher than the condensing temperature the particles "spread thinly" over all levels and that no energy level is occupied by a finite fraction of all the particles .

What do these statements mean?

According to the Bose-Einstein distribution, shouldn’t the average occupancy of the levels be proportional to the energy?
That is, more energy levels are less populated.

And how is it possible that no level is occupied by a finite fraction of all the particles?