The key is derived by PBKDF2 with 1000 iterations. For weaker passwords, I suspect a couple of order of magnitude strengthening would be required.

Your point about weak passwords holds in both ordinary clients and in the browser. It's just a matter of degree. There are plenty of sufficiently strong passwords that are memorable. Since the degree of weakness tolerable is logarithmically proportional to the hashing time and JS is usually within an order of magnitude of native code, the additional entropy required is small given equivalent hashing time.