Usage of monthly indicator variables in a Weekly dataset

I am a newbie and request some inputs on the usage and impact of indicator variables in regression analysis.

I have a weekly dataset and intend to use regression analysis for prediction. To model seasonality, what are the pros/cons of either
a) using 12 monthly (weighted) indicator variables (or)
b) using 51 weekly indicator variables

Will I be able to achieve a similar outcome using (a) or (b). Is there any ways to circumvent overfitment when using weekly indicator variables (point b above), in cases where the dataset is less than a year's worth.