Lucky you!!!
Please keep us updated when you confirm the free shipping to SG if spend above $130, that would be my very first time knowing about an offer of free overseas shipping from Amazon.
I have never come across free overseas shipping on Amazon before, even for small items like CDs. Free shipping is only for domestic US addresses, so I don't think the size of your item matters in that sense. As long as it's outside North America, they will charge shipping.
For some items like books, Amazon is more expensive than the 3rd party merchants selling on Amazon platform. I sincerely believe that the cost of doing business in the US (unless you need to hire lots of labour which is expensive), especially if the systems are automated/machine-operated, is much lower than in SG. That's why so many of their things are so cheap.