Personally, I would first pull the side plate and clean and lubricate the action. Depending on method of carry, exposed hammer revolvers can build up a fair bit of lint and skin cells inside of them.
The next simplest thing would be to replace the hammer/mainspring. Coil springs gradually lose tension from usage/compression cycles.
Not exactly apples to apples, but I replaced the rebound slide spring in a 60 year old Model 10-6 with a 15 lb spring. I'm not exactly sure what the original spring was (modern are said to be 18 lbs), but when I replaced that old compressed coil spring with the 15 lb, there was no change whatsoever in the trigger pull. If it was an 18 lb rebound spring from the start, it sure wasn't 60 years later. I'm fairly certain that one of the previous owners did a whole lot of trigger pulls, as it came to me with a broken DA sear pin.