James,
I think what you might be looking for is scatter coupled with specifying the MarkerColor as a vector corresponding to your linear regression output, g.
Let me show you what I mean using the example data from the biplot documentation (its also 5-dimensional data):
load carsmall
x = [Acceleration Displacement Horsepower MPG Weight];
x = x(all(~isnan(x),2),:);
[coefs,score] = pca(zscore(x));
Now, instead of using biplot, use scatter. The vector g would be the output of your regression model, but here I will just use a dummy vector the same length as my data.
s = 40; %Size of markers, can be a vector or a constant
g = linspace(1,10,length(coefs(:,1))); %Just a dummy g
scatter(coefs(:,1),coefs(:,2),s,g,'fill')
colorbar
You can also do something similar using the MarkerSize vector s, or scale both size and color simultaneously.
Also, this example is for plotting just the first 2 principal components, but if you want to visualize the first 3 principal components, you can use scatter3 and the same workflow described above.
