That's not how a manual transmission works. For a given gear and speed combination, it will always spin at the same RPM. If you see variance, then the clutch is likely slipping.
What you are saying may apply to CVT's though; more load will require more throttle input, which will result in more revs (provided the variator is not locked; AKA 'manual mode' in some CVT transmissions).
Traditional automatics will also slip on more throttle input, as long as the torque converter isn't locked up. In most old school transmissions, there wasn't even a lockup mechanism, so it was always slipping. The slipping is especially noticeable in high stall torque converters, although you will likely never see them in a stock car.