Here's the low-down on volume controls:
On guitars, Volume controls interact with the pickups, the cable and the next device in the chain.
Pickups have a DC resistance, that's the number we see quoted in advertisements. "Our hot humbuckers are wound to 12K." Pickups also have an AC impedance and that varies with frequency. All magnetic pickups have an electrical resonance, usually in the 3KHz to 8KHz range. At resonance, the pickup signal is strongest, and the pickup's output impedance is also at its highest. Any loading of the pickup, whether it's from the Volume control, Tone control, cable, or the stuff on your pedal board, will affect the pickup's frequency response, especially at resonance. It's the resonant peak that is responsible for a large part of a pickup's brightness. Higher value Volume controls provide a lighter load to the pickups and let more of the "sparkle" come thru.
When we turn the Volume control down, we're putting some resistance between the pickups and the cable, and everything downstream of the cable. The Volume control's resistance and the cable capacitance form a low-pass filter which darkens the tone. This is reason for installing a Treble Bleed on a guitar's Volume control. The Treble Bleed helps compensate for the high freq loss in the cable. It's not perfect, but it helps.
When we introduce resistance between the pickups and the first (active) pedal in the chain, we can affect that pedal's behavior. The Fuzz Face is a prime example. It has a very low, non-linear input impedance. It loads the pickups, reducing the treble and creating distortion right at the input of the pedal. When a pedal advertisement touts "responsive to guitar volume," that's one of the reasons why.
In summary, larger value guitar Volume controls can result in a brighter tone and stronger interaction with pedals.
OK, so much for guitar Volume controls, What about pedal volume controls?
Most pedals have their Volume control at the very end of the circuit. Notable exceptions are any pedal with buffered bypass. Pedals generally have a much lower output impedance than pickups. They are less susceptible to loading from the pedal's Volume control. But, the pedal's Volume control will form a low-pass filter with the capacitance of any cable that comes after it. A larger value Volume control will have a lower cutoff freq. The filtering effect is strongest when the volume control is at the electrical midpoint. That's noon with a B-taper pot, but more like 2:30 with an A-taper pot. At 7:00 and 5:00, the volume control's resistance is zero and then it's not part of a low-pass filter. The original Fuzz Faces did not have tone controls or any filtering at the end. Pedal builders installed large value (500K) Volume controls so that they'd get some filtering from the Volume control and the cable capacitance.
Larger value pedal Volume controls result in a darker tone IF the pedal's Volume control is at the very end of the circuit. The pedal's Volume control can also interact with the next pedal in the chain, much like a guitar's volume control.
Lotta words, I know. Hopefully it makes sense.