Model selection with AIC and model efficiency

Starting from an "a priori" set of models based on my knowledge about potential relations between my dependent variable and the independent variables considered, I use AIC to find best models. More specifically I calculate Akaike weights then Evidence Ratio (ER) and consider that models with a ER < 2 are equally likely. But the same problem remain each time I do that. I selected the best models from a set of them, but I don't know if those models are efficient to predict (or at least represent) my data. I can have selected the best element(s) of the list of the worst models.

I do not use $R^2$ in model selection because of the fact that including more variables generally increase $R^2$ value.

But ! When the selection by AIC is done and I can consider that models with a ER < 2 are equally likely. Do you find it is correct to calculate $R^2$ or pseudo-$R^2$ for the best "set of models" in order to have an idea of the representativeness of those models and use this value to select the more efficient model?