[TassyJim]

In terms of hardware I already found what is causing the blank screen:
It happens every time the usb to serial chip (CH340) on the Wemos, activates  the DTR line, which on the Wemos causes that the GPIO0 pin goes to low state. The GPIO0 pin is used as D/C line for the TFT.

Looking at the source code for CumulusMX

comport = new SerialPort(cumulus.ComportName, cumulus.DavisBaudRate, Parity.None, 8, StopBits.One) {Handshake = Handshake.None, DtrEnable = true};

DTR is probably used for genuine Davis equipment which is why it is enabled
I am not sure if there is much you can do about it.

I think I noticed the problem with my setup when I was experimenting but I blamed it on my inexperience and the WeatherDuino normally runs independent of the PC so I didn't look further.

Jim