Question

In a transistor the "base" is made thin while the "collector" is made more doped?​

Answer 1

These bases are lightly doped and very thin, it passes most of the emitter-injected electrons on to the collector. The doping level of collector is intermediate between the heavy doping of emitter and the light doping of the base. The collector is so named because it collects electrons from base.

The Base region is thin so that the majority charge carriers coming from emitter find themselves near the Base collector junction and move to collector instead of going to Base terminal. It is lightly doped so that the depletion region is thin, electric field is strong and the resistance is small.