Source XLR to Balanced Preamp will increase gain?

A properly designed balanced output will be at a higher level than an unbalanced output. I'm not sure it's 6 dB though. I seem to recall once I compared the output of my tuner (it has both balanced and unbalanced outputs) using interstation hiss, and measured the balanced output at 3 dB higher.

Thank You for your perspective on the XLR connections.
The thing that seems tricky is that some CDPs mention the same output level 2.2V (for example) in both RCA and XLR connections while some other CDPs mention exactly twice the output level in XLR compared to RCA. This seem to correspond to the 6db higher output level that you mention here.
From an article on the web, I got this formula:

3dB = doubling the amplitude. If you have a reference signal at 1 volt, 3dB is 2volts, 6dB is 4 volts, and 9dB is 8 volts.

With that in mind, if I choose a CDP with say, 4V output at XLR, will it mean that my amp will ultimately see 8V at the MAX level of the preamp's output?

In many cases, but not always, there will be a 6 db increase going from unbalanced to balanced, everything else being equal. It depends on the designs of both of the interconnected components.

But also, of course, as Jcharvet pointed out different CDPs may have different output levels for the same connector type. So everything else may not be equal.

From an article on the web, I got this formula:

3dB = doubling the amplitude. If you have a reference signal at 1 volt, 3dB is 2volts, 6dB is 4 volts, and 9dB is 8 volts.

That is not correct. A 3 db increase = doubling of power. A 6 db increase = doubling of amplitude/voltage, which corresponds to a 4x increase in power. (As you may recall, power is proportional to voltage squared, for a given impedance).

To be completely precise, this assumes that impedances remain the same as power or voltage is doubled.

Regards,
-- Al

If I choose a CDP with say, 4V output at XLR, will it mean that my amp will ultimately see 8V at the MAX level of the preamp's output?

Assuming you are referring to an active (not passive) preamp, when its volume control is at max its output voltage will usually be several times or more greater than its input voltage, regardless of whether balanced or unbalanced connections are used. In other words, an active preamp applies significant gain to the signal internally, for both types of connections, when its volume control is at max.

Regards,
-- Al

Al,
As always, useful feedback.
I was actually referring to my TVC, which is passive. Yes, active preamps do increase the gain. But since TVCs are just attenuating the voltage, I assumed that the CDP's 4V at XLR, is 4V at each +ve and -ve leg. Hence that would mean 8V at the amp end when the volume on TVC is set to MAX. Is this correct assumption?