I haven't really touched Java in a while but I don't get why you'd want a lightweight DI container . You can just build your object graph and pass dependencies manually if you want a lightweight approach, no? That's just the way people do it in most languages.
In terms of lightweight, I have never needed to use the @Alternative binding [0]. Nearly all of my needs are met by being able to define "this is a singleton, this is a dependency that you should always inject a new instance of, and this is a property."
But it's surprisingly hard to find DI that limits itself like that. The DI in Micronaut and Quarkus are probably the closest to my ideal. Compile time, and only implement a subset of CDI etc.
[0]: https://netbeans.apache.org/kb/docs/javaee/cdi-validate.html