Am I correct that you mean to say that your “1 X 500mV” is 0ne DIVISION at 500mV or 500mV? Or “7 X 500mV” is 3500mV or 3.5 V?
If so, then IC1a pin 1 is 3.5V. Compared to the input of 500mV (0.5V) this is a gain of 7. The gain of IC1a is determined by R3/R2 or 330K/47K which is 7.
Likewise the output level is 2.5 x 500mV (1.25V) compared to the input level 1 x 500mV (0.5 V). So you have measured an overall gain of 1.25/0.5 or 2.5.
The drop in level through the tone section is normal since this is a passive tone section.
Unfortunately, these measurements are only valid for the specific frequency of your sine wave. This circuit famously has a mid frequency “dip” as well as roll-off at the bass and treble frequencies.
Based on your results, I believe that the circuit is performing correctly.