Use Guava's MapMaker.

An example from the doc shows exactly what you need:

ConcurrentMap<Request, Stopwatch> timers = new MapMaker()
    .concurrencyLevel(4)
    .weakKeys()
    .makeMap();

This is, of course, Java, but you can easily wrap this map into Scala map:

import java.{util => ju}
import scala.collection.JavaConverters._
import scala.collection.mutable

val javaMap: ju.Map[String,String] = ...
val scalaMap: mutable.Map[String,String] = javaMap.asScala

Use Guava's MapMaker.

An example from the doc shows exactly what you need (translated into Scala):

import java.util.concurrent.ConcurrentMap

val timers: ConcurrentMap[Request, Stopwatch] = 
    new MapMaker().concurrencyLevel(4).weakKeys.makeMap

This is, of course, Java map, but you can easily wrap it into Scala map:

import java.{util => ju}
import scala.collection.JavaConverters._
import scala.collection.mutable

val javaMap: ju.Map[String,String] = ...
val scalaMap: mutable.Map[String,String] = javaMap.asScala