The 1st portion of your journey is with BA on IST-LHR ; as such the BA baggage rules will apply. For the journey your are doing at that time there is no crossing between IATA areas due to the stopover
Since the journey includes travel to the USA, then this baggage allowance applies to the whole itinerary
BA's allowance is listed at
http://www.britishairways.com/en-au/...age-allowances
Assuming that you are travelling in economy class and that you are not in a Y booking class, then indeed the checked allowance is 1 piece