I think the following will answer both of your questions.
First of all, you select the model that has the minimum value when using such criteria, therefore n has the opposite effect than you wrote down since increase in n alone will decrease the value.
Secondly, and the information criteria is used to select between different models, not to select between different samples. The reason for these criteria to be used is the fact that adding more parameters will always increase the fit however it does not necessarily mean that the model is better due parsimony and degrees of freedom concerns in academy and overfitting concerns in practice.
A criterion such as BIC will be used to compare models that have different variables, where n will be the same. Therefore n is not there to penalize or favor the sample size. I am guessing it is there to normalize RSS, since RSS will increase indefinitely with n. On contrast, adding more parameters is penalized as it increases the value of the criteria.