Don't worry about it, all men have the same issue (correct me if I'm wrong). A consequence of orgasm is that the area becomes very sensistive. The reason why your second orgasm is much weaker and there is less sperm is beacause your testes haven't had time to fully replace the sperm ejaculated first time round. So, in answer to your question, yes it is perfectly normal.

Both men and women experience hyper-sensitivity immediately post-orgasm. Last different times from person to person.

Recovery time time determines the capability for a repeat performance. It is semen production more than sperm production that is the limit. In young men, there is a vast capability to repeat. As a teen, my g/f and I made a bet one night on which of us could bring our b/f's off the most. The guys had to write down the results for reasons they did not know. Between the end of the movie and our curfew, we tied at eight times. In my dumber days, a partner came three times in a condom without withdrawing. NOT RECOMMENDED. There was a pause after each orgasm because of sensitivity for him.

The later ones were getting rather feeble but were still orgasms.