class WeakBoundMethod:

I suggest making it a new-style class by inheriting from object.

    assert (hasattr(meth, '__func__') and hasattr(meth, '__self__')),\
           'Object is not a bound method.'

Don't do this. Just let the invalid parameter types raise attribute errors when you try to fetch the __func__ and __self__. You don't gain anything by checking them beforehand.

assert self.alive(), 'Bound method called on deleted object.'

Raising an Assertion here is a bad choice. Assertions are for thing that should never happen, but having the underlying self object cleaned up doesn't really count. Raise an exception like weakref.ReferenceError. That way a caller can reasonably catch the error.

The documentation is very clear, well done.

class WeakBoundMethod:

I suggest making it a new-style class by inheriting from object.

    assert (hasattr(meth, '__func__') and hasattr(meth, '__self__')),\
           'Object is not a bound method.'

Don't do this. Just let the invalid parameter types raise attribute errors when you try to fetch the __func__ and __self__. You don't gain anything by checking them beforehand.

assert self.alive(), 'Bound method called on deleted object.'

Raising an Assertion here is a bad choice. Assertions are for thing that should never happen, but having the underlying self object cleaned up doesn't really count. Raise an exception like weakref.ReferenceError. That way a caller can reasonably catch the error.

The documentation is very clear, well done.

EDIT

    try:
        return self._func(self._self(), *args, **kw)
    except Exception as e:
        raise e

Why are you catching an exception only to rethrow it? That's really pointless.

I'd write the whole function as:

def __call__(self, *args, **kw):
    _self = self._self()
    if _self is None:
        raise weakref.ReferenceError()

    return self._func(_self, *args, **kw)