Same idea as PgBouncer or PgPool. The advantage over hacking PgBouncer/PgPool for the job is that Tomcat can already do a lot of what you want using built-in, pre-existing functionality. Connection pool management, low level REST-style HTTP processing, JSON handling etc are all done for you.
Yeah, those are nice conveniences but I still think installing Java and getting something to run on startup is a bit more of a hurdle. Better maek life easier up front by having a simple standalone proxy you can compile and run with just whatever is already available on a typical AWS ubuntu environment.
If instead of Tomcat you use Jetty, you can embed the whole app+Jetty+dependencies in a single executable JAR, which easies deployment a lot. Installing a JVM in a Ubuntu environment is just one apt-get and even easier if you use CloudFormation for automation. I don't think is a bad choice at all... you get most of the functionality you want already there, as Craig said, and it's lightweight.