This is what happens with your weights:

>>> list(itertools.accumulate(weights))
[1, 2, 1, 2, 3, 3, 4]

using bisect.bisect certain amount of times, will distribute on this:
a<1<b<2<c<1<d<2<e<3<f<4<g

random numbers between 1 and 2 will go to 1<'b'<2 and not 'd' that is also 1<'d'<2

As discussed in issue31689, if no negative weights should be used, then a ValueError exception should be re-concidered.