Can I split one RS232 output signal into two signals?
You can connect one output to multiple inputs, but you cannot connect multiple outputs to one input.

That means you can connect the line that transmits data from your scales to the PC to a second PC, but you cannot connect the two lines that transmit data from the PCs to the scales.

So yes, you can "tap in" to the transmitted data, as long as you only want to read the data.