Firstly, you've posted this on three different forums - which is firmly against PPrune rules. There are less cuddly moderators than me who would temporarily ban you for that - so I suggest that you either delete two of them, or change them to simple links to the third.
Correcting for weight is technically very straightforward. Standard aerodynamics textbooks will tell you that you can scale inversely with weight, so that
Climb rate at MTOW = (actual climb rate * MTOW / actual weight).
In practice there are too many variables not accounted for by the rather simplistic treatment of most textbooks, for which reason the CAA won't let us use that for more than 5% weight variation in extrapolations. However, for a crude check on "is the climb rate about right", I'd say it's good enough.
The correction for speed however is much more problematic. The speed for best climb will increase with weight - so at the lower weight, the best climb speed will be slightly slower. However, what the actual correction is will depend upon the excess power versus airspeed curve looks like. This is complex, and will depend upon the particular engine / prop / airframe combination - what it is for a 182, I wouldn't dare even guess.
So, if you are looking for a crude check, use the formula shown above. If you want any kind of accuracy, I'd re-do the test at the right weight and speed.
G