Did they ever operate cargo for BY ? What was the reasoning behind ordering them , they must have been heavier than the standard 204s?
Yes, occasionally. Things other than horses, too. I remember we did a series of night newspaper flights LTN - GLA in the early/mid 80s, with about 8 tonnes of papers printed in London for the Scottish market. (To be fair, those were mostly done with pax aircraft, the papers loaded in bundles in the pax seats).
Why buy them? At the time, the government claimed that the BAC-111 would do the same job as the all-pax 737-200 and would impose stiff import duties on the Boeing product. Brtannia argued successfully that there was no QC version of the 111, so 'NA and 'NB were able to avoid the penalty. Yes, they were about a ton heavier in empty weight than the all-pax version.
Also, there were a couple of winters when one of the QC aircraft would be kept in the cargo config for short-notice freight work. My recollection is that not much work came of it.