Changing the weights

Yes, tour playing almost have equal weights; I prefer equal weights as well…different weights could affect off center weights badly.,, IMHO

Fully agree with Chris here. Different weights aren't the best solution. You may want to get fitted for a putter. You may find it as simple as changing to a face-balanced putter over one with a high toe hang or vice versa.

IMO, do not change weights. Scotty knows what he's doing and places them as they should be

I change the weights on my putters but keep the heel and toe the same for consistency. Might consider seeing a PGA teaching pro for a quick putting lesson. Amazing results.

If you are pulling putts, the problem and solution is in the stroke. I recommend seeking some professional help. The sooner the better as putting is key to low scoring. Heavy or light putter, they still need to be balanced and trying to fix a stroke problem with weights will just lead to more inconsistency. A pro will not only help you identify the issue, they will give you some drills to help you ingrain the correct motion so you can fix the problem if it comes back. Hope you get hot worked out as there is no better feeling than to be sinking a lot of putts on the golf course.

Different weights will move the center balance. Try moving the ball slightly back in your setup.

You probably should look into gaming with a different style of putter - with a different hang. Getting refit or get some professional assistance