It is perhaps one of the most famous quotes in the Jurassic Park movie:
Can anyone please tell me what it means exactly?
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I don't recall the context in the movie, but in general:
cheap: inexpensive or of poor quality.
I got an extra dozen eggs this week because they were cheap.
I didn't buy the bookcase because it looked flimsy and cheap.
slang: "cheap shot" is a verbal or physical attack that is very easy and considered cheating)
The comment about Andy's hair was a cheap shot, he already feels bad about it.
"Cheap" can refer to either the cost of a thing, or to describe a person that only likes cheap things.
My Dad is too cheap to buy new paint.
"Don't _ on me": Don't do this around me or to me or in a way that affects me.
Don't eat all the ice cream on me.
So the phrase "Don't get cheap on me." could mean one of: