Hey @shpider ! Did you happen to measure your TP Spring before you installed it? Just curious about the overall length, compressed length and strength of the spring.
I picked two springs up from one of the local hardware stores for $0.98 and $0.79 to play around with. They had a whole bunch of different lengths, diameters, tensions!
The $0.98 one is 3-1/4" long, compresses to 1-1/2" long (nearly lost an eye figuring that measurement out), 3/4" in diameter, and is quite... enthusiastic about not being compressed with only two fingers!
The $0.79 one is 2-7/8" long, compresses to 5/8" long, 13/16" in diameter, and is much less of a workout and way more fun to just squish between your fingers.
The answer to all of your Toilet Paper Roller questions can be seen in the pictures below... It's very easy to compress between my right thumb and 2 fingers (no, I don't only have 2 fingers and a thumb... I have 6 like everyone else!)
I think the important thing to note is the number of coils... this has very few making it a very soft spring... It really doesn't take much to spring the chamber open...