When I click Send/Recv, it looks as if Outlook checks the same account
twice. What could be the reason? As far as I know I did not add the
same account twice (if that would be possible at all). It is not a
big problem, but it seems a loss of time.

How many accounts do you have defined in your Send/Receive group? If more
than one, do any two or more of them use the same username/password to
connect to their servers?

I have two accounts with each a different username & password. When I click
send/receive only the default account is checked; for the other one I have
to 'ask' specifically.