this is a solvable problem.
I guess your MSP430 can communicate over a standard serial UART-interface.
At a low baudrate this can be done in complete software without any special-purpose-hardware-UART-interface inside of the MSP430
Even if you would have to send 1 kB of sensordata very often even at a slow baudrate of 9600 baud this would be done within 1024 Byte * 11 Bit / 9600 baud = 1,2 seconds
instead of reading the BMP280-sensor you wold receive the sensor-data over the serial connection and the rest is done by the ESP8266
like desceribed in this tutorial
best regards Stefan