Hi,
In their 1926 brochure, Douglas say that the 350 EW has a 60.8 x 60mm engine of approximately 348cc developing well over 10 bhp (but do not give the actual figure). There is no mention of the weight of the machine, but the later version - the A28 is listed as being under 200lbs (this is presumably without lights or horn, as they are listed as extras). The following year, the same model (now designated the A29) is listed as being 3.5 hp (presumably, this is the old RAC rating).
Hope this is of some help,
Regards,
Eddie.