Is it inherently invalid to use BIC for model averaging? If I understand AIC/AICc vs. BIC correctly, AIC presumes that there is no "true" model and that any given model is simply a "best worst approximation". However, BIC presumes that there IS a "true" model and that the lowest BIC of a comparison represents the best approximation of the models present of that "true" model.
So, why do people use BIC for model averaging? Doesn't that contradict an important assumption behind BIC? Is it merely because BIC penalizes more harshly for additional terms? If so, does that mean the premise of a "true" model really doesn't matter?
 A: BIC assumes a true model, but you don't know what that model is.
Let's take a step back (and assume we're being Bayesians while we're at it).
Imagine we're trying to forecast where the true model is among a collection of possible models (the situation the BIC is for). We don't know which model is correct, so we can only update our prior probabilities on the models to posterior probabilities (given the data).
So imagine we have 48% posterior probability on one model, 39% posterior probability on a second model, and 12% on a third (with all other models in the collection sharing the remainder which I'll mostly ignore for now). 
We want to make a forecast (e.g. give a 95% posterior prediction interval) that incorporates our uncertainty about which model is correct. Note that if we (quite incorrectly!) treat the model with the highest posterior probability as if it were known to be the model, we'd be asserting a level of certainty about our forecast interval we don't possess; it's conditional on a model being the correct one that we don't have good reason to say is the correct one. Indeed we are slightly more certain that particular model isn't the right model than we are that it is (our posterior probability that the first model is not the right model is 52%). 
It would be reckless to ignore that uncertainty about which model is the correct one -- our forecast interval would be too narrow (often far too narrow). 
Now BIC is (up to a common shift) minus twice an asymptotic approximation to the posterior probability (under the assumption of equal prior weight). So model averaging weights derived from BIC in the usual way correspond to posterior probabilities under a particular set of assumptions (including that there is one correct model). The same argument I gave above applies -- we don't know which one it is, and it would be reckless (indeed, quite wrong) to pretend we did.
It's not much different to saying "I know the population mean has one particular value" and then complaining when people want to give an interval for it (we don't know what they value is, so of course it's reasonable to entertain more than one possible value in our inference).
