I would like to compare models (using AIC and AIC weights) in which a 2nd and 3rd predictor is added to a base model that has just 1 predictor. I'm confused on how to specify the simpler models. If the base model is "Y on P;" and the 2nd model is "Y on P C;" (C is a control variable), then the base model has a better (lower) AIC and an AIC weight of 1 (i.e., they're not even close), even though the R-squared is better (higher) in the 2nd model. Should C be in the base model? (if so, how exactly?).
The 3rd model introduces a mediator: "Y on P C M;" "M on P C;". If the comparison model is "Y on P C;", then the simpler model is preferred again. I want to make sure I'm doing this right before I interpret these results.