Improving SNR by increasing resistor value
All resistors produce the same noise power.
If the measuring system has a higher input resistance than the resistor, which is often the case, then the noise is predominantly a voltage measurement, and reducing the resistor will lower the noise voltage.
The converse is true for current. And measured into a matched load, the received noise power is independent of the resistor value.
3dB is an approximation for half power (it's 3.010 to a few more decimal places).
Regardless of the initial resistor value, if changing the ratios produces half the noise power, you'll get 3dB.