... This is purely from a hobbyist point of view, working with layouts as guide.
I too started understanding amps with layouts. If you want to get somewhere, you'll have to go way beyond that, and learn some basic theory of how electricity & electronics work. The first 4 modules of
NEETS will get you started (I'm sure you'll wander to a couple of the other modules).
I'm at a point where I don't like working from layouts; they just show me "this connects to that." Schematics show you how a circuit is arranged, without the issues of physical spacing, tube pinouts, etc.
... I don't quite understand what makes the wattage work and I am curious to know if I could put in other tubes and a new transformer to make the Blues Jr a bit louder.
Power = Voltage * Current.
That equation can be manipulated with algebra to arrange it in different forms. We might combine it with Ohm's Law, Voltage = Current * Resistance; might might use algebra to rearrange either or both equations to solve for what we need to know.
If Power = Voltage * Current, and we need double-power but Voltage stays unchanged (perhaps because we're already using a voltage as high as practical or which the tubes will allow, which is typical in many guitar amps), then it should be obvious Current must double.
2*Power = Voltage * (2*Current)
How do you get the "2*Current" to happen? Let's rearrange the formula for Ohm's Law noted earlier. Current = Voltage/Resistance. To get "2*Current" to happen, we need half-Resistance:
2*Current = Voltage/(0.5*Resistance)
The PT determines the voltage available, but the high-voltage winding has a specific rated current capability. So for the 2*Current to occur, the new PT needs same-voltage and double-current of the original.
But what's the "Resistance"? It's the OT primary impedance. If supply voltage stays the same, the OT primary impedance must drop by half, or no additional current can flow.
And the output tubes are the medium by which we draw current from the PT and control its flow through the OT primary impedance. So the output tubes need to be capable of the new 2*Current as well. Amp manufacturers don't typically leave a lot of unused capability, in the output tubes, so we probably will need either twice as many of the same tube-type, or same-number of a bigger type which can pass 2*Current.
Prove the above by plugging in some numbers. Let's say your Blues Jr has 43mA RMS through the entire OT primary of 8kΩ in its original configuration.
Power = Voltage * Current, and Voltage = Current * Resistance, so Power = Current
2*Resistance = (0.043A)
2*8kΩ = ~15w.
If we halve OT primary impedance and double current, we get Power = Current
2*Resistance = (0.086A)
2*4kΩ = ~30w.
So the answer is you need a PT with same-voltage and double the current capacity, an OT with half the primary impedance, and twice as many (EL84 or 6V6) output tubes or same-number of a bigger tube type (like 2x EL34's or 2x 6L6's).