People have reported very good low memory performance using Scalatra. One example write-up is at:
http://fehguy.tumblr.com/post/33760322808/my-house-heater-has-a-rest-api-with-phidgets-scala
Memory usage figures as low as ~30MB to ~40MB have been bandied about in blog posts and IRC conversations.
Some tips:
1) Scalatra allows you to select exactly the dependencies you want. The core HTTP router will work just fine on a Raspberry Pi - be extremely careful with selecting additional libraries and benchmark your memory usage whenever you add a new jar.
2) The current Scalatra g8 template will, by default, wire up precompiled Scalate templates for you. These are fine on a normal server, and it's usually very convenient to have things set up for you already, but in a memory-constrained environment they are the first thing you'll want to look at either ditching or optimising.
3) At least three people in the #scalatra irc channel on Freenode have already experimented with running it on a Pi, so depending on your use cases(s) their pain may be your gain.
4) You'll get the best possible memory consumption by launching your Scalatra app as a standalone Jetty servlet. This is detailed in the Scalatra standalone deployment guide.