Does Amazon have a sweetheart deal with USPS?

The US Postal Service has lost significant sums of money every year for at least a decade.  President Trump claims that USPS's contract with Amazon has made things worse.  This article in VOX provides some insights to help analyze Trump's claim.  Key takeaways:

1. Shipping and packages is the only major component of USPS's revenue stream that is increasing, growing by $2 b in 2017 over 2016.  
2. First class mail and marketing mail revenue are down by $3 b over the same period.  
3. USPS costs are largely fixed.  Delivery takes place over the same routes every day; the same sorting and shipping operations take place each day as well, subject to some seasonal fluctuations.  
4. Unlike any private company, USPS must pre-fund its pension and retiree health benefits for the next 75 years.  This costs $6b annually and accounts for most of USPS annual losses.  

As long as the Amazon contract covers the variable costs of weekend deliveries, USPS comes out ahead.  Could USPS charge Amazon a higher rate?  That depends on whether Amazon could find close substitutes for package delivery.  I would not underestimate them.