My Passport has a stamp of Indian visa on it which is good until next week. Can I use this visa to travel for the next six weeks?
A visa normally has an expiration date which determines the last day that you can enter one country. The expiration date does not affect the duration of your stay because this can be limited by a particular immigration officer when you arrive. If in case you cannot enter India, and this situation happens before the visa expires, then you need to request for another one.
If you are located in the United States and have more questions, you can contact Travisa office (This office is the outsourcing group which handles Indian visa applications and assists Indian Embassy as well as their consulates which are in the United States. Yes. They are in India!)