I do not have your product, but Adsafruit's. I know you contributed 99% of the design. I didn't know that till after I bought the ESP8266 HUZZAH board and display and read the tutorial. It doesn't seem like they are supporting it very well, for now it's a bit old. Anyway, had a bit of trouble getting it working. It does now, except for one problem and Adafruit seems stumped.
I apply power, 5 volts or Li-Po battery. Screen goes white. After about 18 seconds, it goes dark and stays dark. If I push either Reset button, program starts right up. From then on no problem. Shows weather for about 12 seconds, then goes dark. Touching screen starts update. But, if I kill power and re-apply, same thing happens, I must use reset button. I am wondering if the ESP8266 might be an incorrect version? It is a ESP8266-F, instead of the -12 or -12 S one normally sees? Maybe I need some amount of delay in Setup, but now sure where to put it.