First, a note on Pushoff. Many people will recomend to check for pushoff without mentioning the potential that exists for creating this problem simply by testing for it. IF YOU PUSH TOO HARD YOU CAN CREATE PUSHOFF IN A REVOLVER THAT PREVIOUSLY WAS WORKING PERFECTLY. Limit any force applied to just the weight of the gun. Basically, balance it on your thumb with the barrel pointing straight up and see if the hammer releases. Yeah, a VERY conservative test but it's better to be conservative instead of causing enough damage that the only repair option is to replace both the hammer and trigger. Most gunshops won't object to a balance test for pushoff, however if they see you trying to push the hammer off with force they may take it from your hands and beat you senseless with it.
Historically, the SA trigger pull on a S&W revolver was lightened by stoning the SA sear on the trigger to what I call an "assist" angle. Basically, the sear is "sloped" slightly in a way that the sear on the hammer is "sliding downhill". This is a practice the is NOT necessary today and a practice that I do NOT endorse. Because it puts ALL the wear on the tip of the sear on the hammer and WILL lead to pushoff as the sear on the hammer wears.
Today the best way to adjust the SA trigger weight is by changing the rebound spring. I've found that a 14 lbs. rebound spring will result in a 3 lbs. SA trigger pull in most cases, provided the DA trigger pull has been tuned to the 8-9 lbs range. Because there is some interplay between the mainspring tension and the SA trigger weight you do have to do a bit of back and forth when selecting the correct rebound spring. However, even with the mainspring producing a 12 lbs. DA trigger pull a 14 lbs. rebound spring will result in an SA trigger pull in the 3 1/4 to 3 1/2 lbs. range. So, mainspring power only has a minor effect on the SA trigger weight. What has the greatest effect is the rebound spring and whether the SA sear on the trigger has been reground to an assist angle.
Obviously, a good trigger pull gage is a very useful item to own when working on these triggers. The one I like is the Lyman Digital, at about 70 dollars it's not hugely expensive and I've found it easy to get repeatable results with. However, it's maximum limit for weight is only 12 lbs. and some new S&W revolvers are shipping with DA triggers over 12 lbs., so caution must be used if checking the DA trigger on a brand new S&W.
An alternative to using a trigger gage is a simple string with a known weight attached to it. To make up those weight you can use a basic and cheap Postal scale, just start stringing large nuts or anything handy and weigh it. Take a bit of hanger wire, bend it to a hook to engage the trigger and make a loop for the string that is located behind the frame. BTW, add that bit of wire to your weights so you include it's weight in the total.
Now that you are set up to determine the true break of your trigger it's time to see where it is. Personally, I strongly prefer a 3 lbs. SA trigger, which some may consider a bit light. Out of the box a factory new S&W revolver today will have a SA trigger in the 4 1/4 to 4 1/2 lbs. range. Take that factory new revolver and install a much lighter 12 lbs. rebound spring in it without doing anything else and you should see a SA trigger in the 2 1/2 lbs. range. Tune the DA trigger to 8 lbs. and it will only drop to 2 1/4 lbs. If you see a SA trigger BELOW 2 1/4 lbs. it's near certain the SA sear on the trigger has been stoned to an assist angle no matter what rebound spring is installed.
This means you will need to re-sharpen the SA sear on the trigger before doing anything else. I'll also note that any gun that was used a lot in single action with an assist angle on the trigger sear WILL need to have the hammer replaced because it's been "worn in" to match than assist angle on the trigger sear. Since the total length of the sear on the hammer is only about 0.005 inch, reshaping that surface is not an option. Now you know why I will NEVER endorse re-shaping the sear on the trigger to an assist angle, hammers aren't cheap and can be difficult to find.
If you find you need to "sharpen" the sear on the trigger there are two things to keep in mind. One is that trigger is likely to be case hardened and that hard casing is likely to be about 0.015 inch deep, a common casing thickness for case hardening steels. So, take a LESS IS BEST approach to try and avoid stoning thru the case hardening. That means STOPPING AS SOON as you see that fresh surface evenly meet the tip of the sear and going no further. Second, see the link below for what I consider the ideal jug for stoning this sear. Note, you'll also want to do your stoning using only about 1/4 inch on the tip of a 6 inch long stone, meaning short back and forth strokes.
http://smith-wessonforum.com/s-w-smithing/195061-tuning-jigs.html
PS; kudo's to Gizamo for posting a superb idea and illustration for a trigger tuning jig.
PSS; By formal definition a "hair trigger" is a trigger with very little Sear Creep and weight is NOT a factor in this. Basically, you can have a 50 lbs. trigger pull in a "hair trigger", what makes it a "hair" is that the total amount of movement is about the thickness of a human hair. Normally in the larger S&W frame sizes the total amount of Sear Creep on the trigger is between 0.015 and 0.018 inch, so they are all quite close to being "hair triggers".