If you've got some aid you need to distribute then obviously you could just distribute the aid to the people. Maybe pay a person a salary to run a team to work out who gets what.
But that would be "big state".
Instead it's more efficient to just hand the money to a limited private enterprise and ask THEM to pay a person a salary to run a team to work out who gets what. And of course don't forget to skim a bit off the top for your shareholders.
That is "little state" because it costs more and helps support capitalism and conservative party donors.