Don't confuse "bought it up" with "bought it" - they are entirely different idioms.
Your reference is to "bought it" which is an idiom meaning 'to die'; frequently used in war films, etc.
There's an invisible comma separating the ideas.
We thought you bought it, up there.
There's a long version - 'to have bought the farm' - though I don't know which came first, or if one is a short form of the other, or one is a long form...
There's an additional meaning, which you would have to extract from context, "bought it" can also mean to believe something.
I told him the lie & he bought it.
By extension, there's a movie term meaning to accept that take [current version of the scene being filmed] & be moving on to the next setup.
Did they like the take?
Yeah, they bought it, we're moving on.
"Bought it up" however, really does mean 'to purchase', though it hints towards 'all' of something.
Are they really building a motorway where your street is?
Yeah, the government bought it up.
The government bought the entire street & surrounding land.