Apart from the absolute value of the weight lifted, beyond a point of time there's also a diminishing strength return with increasing bodyweight (although strength DOES increase) - this makes it easier for lighter guys to lift x times their bodyweight than bigger guys. Therefore for "best lifter" comparisons, Wilks coefficients are widely used in a powerlifting meet.
Mathematically, Wilks coefficient (comparing relative strength of PL) is given by the following formula:
coeff = Wt lifted / (a + b*x + c*x^2 + d*x^3 + e*x^4 + f*x^5)
Here x is the bodyweight and a-f are constant values (different for men and women). As you can see, the variation is non-linear. The normalized weight is this factor multiplied by the weight lifted.
Here's a graph I plotted out (lol, I have nothing better to do at lunch time), which shows the variation of normalized weight with bodyweight if the lifters lift 2x bodyweight.
Lifting 2x stronger at a higher bodyweight would have you much stronger compared to a lower bodyweight using the normalized scale.
In your example, normalized weight lifted by the 180 lb lifter lifting 360 lbs would be 242.712. The same value for the 350 lb guy lifting 600 would be 327.9