Mean exceedance for Bernoulli sums with two equal exceptional weights

This preprint presents a provisional candidate theorem for independent Bernoulli(p) variables with nonnegative weights consisting of two equal exceptional weights and n equal ordinary weights, where n >= 1 and 2a + nb = 1. It gives a written proof of the mean-exceedance bound P[a(B0 + B1) + b sum(Bi, i=2,...,n+1) >= p] >= p for 0 <= p <= 1/3; the event may be replaced by strict exceedance for 0 < p < 1/3. The exceptional weights may be larger or smaller than the ordinary weight. The argument combines a binomial-median and reflected-tail comparison with a capacity reduction and exact small-ratio identities. Together with the earlier one-exceptional-weight result, it covers vectors whose positive entries take one value, or exactly two values with at least one positive-value class occurring at most twice. The supporting archive includes the article, source, exact finite checks, and reproducibility records. The finite checks do not establish the infinite parameter range, and the general weight conjecture remains open.