IIRC the Model 52 thumb safety is strictly within the slide. When you apply the safety part of the through rod rolls down and keeps the hammer from hitting the firing pin. This is what allows you to dry fire it without damage. As such, it should not affect the weight of the trigger pull.
The early 52s used the same lockwork as the Model 39. This could be adjusted for either single action or double action using a socket head screw in the frame. The first thing to check is to see if it will operate single action. Don't laugh, but check it when it is held upside down as well as right side up. If it doesn't work take the slide off, find the socket head screw, tighten it down snugly, and see if that makes a difference. The position of that screw is what determines if you are firing single action or double action where the pull would be much higher.
My 52 worked well for years and then wouldn't fire at all. It turned out that vibration had loosened that socket head screw causing it to back out somewhat. (and yes, it would work it the gun was held upside down) It now sports a new screw that bottoms out an the bottom of the screwhole instead of at the top and had the head shortened to get the release I wanted. I watched while my gunsmith worked on it and got a lot of practice disassembling and reassembling all of the lockwork. Hope this helps.
EDIT The screw I am talking about is No. 82 on the diagram Mike linked to.
