That should work fine.
Delays are not needed, when you use the Serial.write() instruction all it does is pass the value to the UART transmit register. The UART then adds the start, parity and stop bit and sends it one bit at a time out of the TX pin. The UART has a status bit that tells the program whether it is still sending the previous data or if it is free to accept some more. The Serial.write() checks that bit and makes sure it is safe to feed it the next character to be sent.
The only thing you might have to do is add another character or two to the end. When you used the scales, your terminal probably showed something like this:
N+123.456g
N+654.321g
N+001.234g
with each result on it's own line rather than N+123.456gN+654.321gN+001.234g with no gaps between readings.
The reason would be that there is probably a carriage return and line feed character after the characters you can see. They are not visible in a terminal program because all they do is move the cursor down to the beginning of the following line. If you need them, just add two more lines to your commands:
Serial.write(0x0A);
Serial.write(0x0D);
and that should fix it.
Brian.