It's tough to give you a definitive answer, so I'll lay out three strong possibilities.
1) Simpson's Paradox
This is the first term that comes to mind. This refers to a situation where a trend appears in different subsets, but disappears or reverses when these groups are combined.
The term is also used to refer to an overall trend that disappears or reversed once it is broken apart by some third variable.
One of the most famous cases of Simpson's paradox was the illusion of gender bias in the admission to UC Berkeley. Once the gender data were broken apart by department, the trend reversed.
I think that's pretty close to what you're observing. You're finding a correlation that disappears when you subset by a group.
However, there are a few other ways to explain what you're seeing.
2) Mediator effect
This term refers to a third variable that explains the relationship between an independent variable and a dependent variable. In this case, your mediator would be "weight."
Note that in order for weight to be a proper mediator, you'd have to establish an actual relationship between weight and your other two variables. Check out the Sobel test for more info.
You could be describing a case of full mediation, but only if you think weight fully explains the relationship between X and Y.
However, because I don't exactly how these variables are related, you should keep reading! There's more!
3) Moderator effect
This term refers to when a third variable effects the strength of the relationship between two variables. The third variable is referred to as the moderator variable or simply the moderator.
You could definitely argue that weight category moderated the relationship between X and Y.
My guess: weight was acting as a moderator, but I'll leave any further investigations up to you!