I can't speak for Vayama, but it's possible you're on some discount biz ticket and changing the return by a week forces a reprice into a much higher fare class. Full J on the route is around 7-10k USD I'd assume. $4,700 USD for a round-trip from SFO does sound like low to mid-priced ticket for the route.
It's also possible just the flights you asked for aren't available in your cheap fareclass, This would be a better situation for you. Maybe you can just see if a different flight or different day will give you the original ticket pricing.
If you don't show up for your next sector, the rest of the itinerary will cancel.
Lesson for the future, if you're spending multiple thousands or more on tickets, don't use discount online travel agents unless it's Amex, or a premium one you have a relationship with.
Sounds crappy.