From the very same page, section Why Weak Map?:

The experienced JavaScript programmer will notice that this API could
be implemented in JavaScript with two arrays (one for keys, one for
values) shared by the 4 API methods. Such an implementation would have
two main inconveniences. The first one is an O(n) search (n being the
number of keys in the map). The second one is a memory leak issue.
With manually written maps, the array of keys would keep references to
key objects, preventing them from being garbage collected. In native
WeakMaps, references to key objects are held weakly, which means
that they do not prevent garbage collection in case there would be no
other reference to the object.

Because of references being weak, WeakMap keys are not enumerable
(i.e. there is no method giving you a list of the keys). If they were,
the list would depend on the state of garbage collection, introducing
non-determinism.

[And that's why they have no size property as well]

If you want to have a list of keys, you should
maintain it yourself. There is also an ECMAScript
proposal
aiming at introducing simple sets and maps which would not use weak
references and would be enumerable.

‐ which would be the normal Maps. Not mentioned at MDN, but in the harmony proposal, those also have items, keys and values generator methods and implement the Iterator interface.