Different weight and brands of ammo will shoot to slightly different points of aim. You can always try a few different loads in a particular gun. One might be right.
While this would be a LAST resort, you actually can adjust the point of impact with a file. The sight track can be opened up one way or the other, and the front sight can be filed down or thinned on either side. I know you can not increase the front sight height, but you can lower the rear notch, which is has the same effect of raising the front sight. I hate to take a file to a fixed sight gun, but once in a blue moon it is necessary. I have done this only once and it was on a clone of a Colt SAA revolver made by Umberti. Being that it was not a genuine Colt, I did not loose sleep over it and it did work very nicely.
I own a bunch of 2" Chief's, a M60, M36, M37 etc, and my choice for pocket carry is the M60. It is just easier to shoot Buffalo Bore 158grain +P ammo in, and the extra 4 ounces does not bother me. The only time I carry the M37 is when I wear a suit or dress pants that are thinner and pull easier.
Personally, if after trying different ammo and bullets it did not solve your problem, I would use a file to correct the point of impact rather than to smack the barrel with a Babbitt! Remember that when you have such a small stubby barrel you would have to move the barrel quite a bit to change the impact that much, which in turn (IMHO) affect the thread alignment.
Chief38