You’re developing a working intuition quickly 
I mentioned an expected 1.6 V earlier, and since this thread is as much about “beginnings” as this specific circuit, I thought I’d “show my work”:
The output part of this circuit is a voltage divider (yes, there it is again!) where the output voltage depends on the resistance below the output pin, in relation to the total resistance. If we pretend that the transistor is theoretically ideal and always fully on (0 ohm), the source, drain, and output voltages will all be the same, and the output is set by R5 and R1 only:
- with R5 at 1k, source and drain and output will be 9V×1k/(1k+1k) = 4.5 V (if both resistors are the same, they split the voltage in half)
- with 4.7k, they’ll be 9V×1k/(4.7k+1k) = 1.6 V
- with 10k, they’ll be 9V×1k/(10k+1k) = 0.8 V
- with 47k, they’ll be 9V×1k/(47k+1k) = 0.2 V
Your measurements are a bit higher than these values, which means that the JFET is adding some resistance to the circuit, shifting the output higher.
To get from 4.5 V to 6.3 V it needs to add 1.3k to the circuit (9V×2.3k/(1k+2.3k)=6.3V), to get from 0.8 V to 1.2 V it needs to add 540 ohm, etc.
Note how this resistance varies, even with a fixed input – the JFET’s drain-source resistance depends on the voltage difference between gate and source, i.e. the voltage across R1 – but that voltage depends not only on the values of R1 and R5, but also on what the transistor is doing. If the drain-source resistance goes up, the R1 voltage drops.
Yep, you read that right – what the transistor is doing depends on what the transistor is doing.
In practice, the transistor will find the right balance and stay there, and you can get some idea of where you’ll land from the datasheets, but things aren’t very exact. Here’s an excerpt from a 2N5457 datasheet:
I’ve highlighted two values that are important for this kind of amplifier; the gate-source voltage difference where the transistor cuts off completely, and the drain-source current at zero gate-source voltage difference.
Note the wide min-max range – these components are absurdly imprecise on their own. Given modern manufacturing standards, two transistors from the same production batch are probably rather close to each other, and often close to the “typical” value if there is one, but transistors from different batches/plants/manufacturers can vary a lot.
Relying on vaguely defined parameters is a very stompbox thing, of course, and mostly by tradition – many early designs were pretty haphazardly put together, for a variety of reasons, ranging from economics and component sourcing contraints, to people having absolutely no idea what they’re doing 
Which is part of the fun, obviously, but can also be immensely frustrating, especially if you try to build two or more of something. And if you look at stompbox forums, it often leads to insane amounts of cargo culting.
(In JFET opamps, there’s additional circuitry to force the input JFETs to behave more consistently, and they use multiple amplifier stages to better control what’s going on instead of trying to get a single transistor to do everything. Also, opamp amplifier designs use negative feedback to further constrain the behaviour, bringing everything into much more well-defined regions. You can still do soft/hard clipping, but you do that by bringing the signal levels into the right range before the diode stage so you hit the diode’s “voltage-controlled resistor” knee at the right place, instead of trying to bring the diodes to the levels you have in the circuit for other reasons.)