Is it even legal for them to collect such hefty fees for such small quantities ? Even in court the amount is some 10k fine for personal quantities. You may wanna consult a lawyer but then lawyer fees is gonna be there too. Looks like you're stuck in a tight spot mate.

If it was a single room and the weed was found in your room, you can effectively say the other guy isn't at fault and reduce it by half but if it's a shared room, one of you guys have to take the blame. That way atleast you reduce the fine by half and if they're gonna drug test or something, the other person can always say he smoked outside campus grounds where the institute doesn't have any jurisdiction.

The other option is to borrow money from some relative or a wealthy close friend and pay the fine, get done with your masters and leave the institute. And also if you had dreams of doing a PhD that's almost a pipe dream at this point cuz even your PI won't give you a good LOR. So yeah best option is, borrow money, pay fine, finish masters, get a job and pay back what you borrowed. There's no other way out.

Also, you've learnt your lesson. Trust no one when it comes to disclosing that you smoke weed. "Our batchmates are all very good friends with us" is valid only until any of them get into trouble and have to choose between their future or ratting you out to the authorities. You know what they're gonna choose cuz if you're in that spot, you'll do the same.