On your Pro Micro, is the metal can engraved with "16.000" like the one in the picture you shared, or does it say something like "8.000"?
There are 16 MHz and 8 MHz Pro Micros and if you have a 16 MHz board selected from the Arduino IDE's Tools > Board menu when uploading to an 8 MHz board, or vice versa, then it will cause the exact symptoms you have described.