I'm unfamiliar with your content just commenting as a player and dev myself, I for one do not have any problem with weekly, monthly, or even yearly releases of a game. I think splitting into different releases has benefits; allows you to start small and get a proper hang on the mechanics and code, keeping players invested, giving you more time to work on it, allowing for more accurate feedback via existing chapters. However consistency is important and be sure to update your players when you intend to release future installments. And try to keep the plot and mechanics similar between chapters or players will feel alienated.
My opinion: By all means go for it.