Bitbucket On-Prem (aka Bitbucket Server) is pure Java + direct git invocations, so runs very nicely on modest hardware. Can get by on 1GB RAM! (But more recommended if you have more than 10 users).
Doesn't it require Tomcat, Apache, Postgres/MySQL? I've recently installed Jira Core and Confluece for a client and they hardly seem lightweight web apps.