Having a WeakReference with varying levels of weakness (priority) sounds nice, but also might make the GC's job harder, not easier. (I've no idea on the GC internals, but) I would assume there some sort of additional access statistics that are kept for WeakReference objects so that the GC can clean them up efficiently (e.g. it might get rid of the least-used items first).
More than likely the added complexity wouldn't make anything any more efficient because the most efficient way is to get rid of infrequently used WeakReferences first. If you could assign a priority, how would you do it? This smells like a premature optimization: the programmer doesn't really know most of the time and is guessing; the result is a slower GC collection cycle that is probably reclaiming the wrong objects.
It begs the question though, that if you care about the WeakReference.Target object being reclaimed, is it really a good use of WeakReference?
It's like a cache. You shove stuff into the cache and ask the cache to make it stale after x minutes, but most caches never guarantee to keep it around at all. It just guarantees that if it does, it will expire it according to the policy requested.