k is the number of factors you have in the model. Since you’re doing PCA first, it will depend on how many components you show the model. You take your 3 time series and form three principal components, then decide how many to include in the regression.
If you want to select among a large number of explanatory variables, you might consider just using highly skeptical priors (like Laplace) and including all your data. Bayesian regression with priors can be see as a special case of ridge regression (or the other way around?), so variables with low explanatory power will see their coefficients “shrunk” towards zero. I admit I don’t totally understand the weighting scheme you describe, though, so this might not be what you want to achieve.
I’d also encourage you to consider a more robust evaluation metric than R squared, like some kind of out-of-sample error. R squared can be juiced up as high as you’d like, and won’t give you any indication about your model’s ability to generalize (forecast).