How to remove the effect of one variable by using linear model residuals My data set has species with a number of morphological variables, including body mass:
species  mass  skull  wing
a        10     4      4
b        15     3      5
c        30     2      6
d        40     5      9 

But I want to look at a PCA of my data while controlling for body mass.
Is it appropriate to conduct regression models of skull ~ body mass & wing ~ body mass and use the residuals of these models in my PCA?
 A: (Summarized from discussion in the comments.)
PCA finds the largest variance among combinations of the input variables, so I'm having a hard time imagining the benefit of this approach. Since your variable for body weight is on a different scale (about an order of magnitude greater than the other variables), you should instead consider scaling your variables, such that their variance is the same.
You mention that body weight affects each of the other variables, but this doesn't have to be a problem: The first principal component will then likely be some combination of bodyweight and the other variables, explaining the larger part of the total variance (you can confirm this by inspecting the size of the loadings for body weight in each PC). If you are not interested in body weight per se, you can look at the remaining principal components.
A: I'm going to assume you have several other body parts, otherwise, there's not much point to PCA. 
If you  do PCA on your full data set, then what is likely to happen is that the first component will be an overall body size measure. Then you can just look at your second, third etc. components and see what they are. 
The issue of different scales can (as per the comments) be dealt with by scaling the variables first. 
Finally, I think you might want factor analysis rather than PCA. 
