Hi Paula,
Climate wise, the weather on the Azores is mild, the closest comparison would be Madeira. The weather is very localised - it can be hot with bright sunshine on the coast, whilst up in the hills and mountains only a few miles away it can be several degrees cooler with rain and mist. It is not unusual to experience four seasons in one day. Rain can suddenly start and as just as suddenly stop. The best approach to take is to dress in layers and add on or take off as necessary.
Temperatures are hotter and more humid during the summer months (June-October) when it can reach 25 degrees Centigrade. Rain never lasts long in the summer months. 
With an average of 21 degrees, many different flowers are blooming throughout September. Some places even grow Tea, Bananas, pineapples, pepper and Tobacco.
I would suggest just to take light clothing such as t-shirts, vest tops, linen trousers, skirts and flip flops. It sounds like the weather is going to be like a nice summers day in England so I would pack enough light clothing to last you plus a few cardigans etc, just in case!
Your hotel, The Hotel Bahia Palace is surrounded by green hills and blue sea, the Bahia Palace Hotel is located on the beautiful Sao Miguel Island in the Azores archipelago. It has:
Billiards 
Cocktail bar 
Disabled facilities 
Gymnasium 
Internet access 
Laundry facilities 
Restaurant 
Sauna 
Swimming pool 
Table tennis 
Tennis court 
Your room will have:
Air conditioning 
Balcony / Terrace 
Cable / Satellite TV 
Hairdryer 
In-room safe 
Private bathroom / Ensuite 
Telephone 
Voice mail 
I hope this helps. If you need anymore information on your holiday or your hotel, please let me know, will be happy to help.
Warm wishes,
Cheryl, your editor