Ships going over the horizon

Hello fellow skeptics. Ships supposedly go over the horizon. This means the earth curves *down* at that point, where the ship disappears. How can the horizon rise at all if we go higher? Globe believers claim it does not rise to eye level, but I think it should not rise at all but stay fixed. How would the horizon appear on a globe earth as we ascend? Also wouldn’t the earth be smaller if it curves at the horizon? This is an honest question, I’m trying to understand. Thank you.