Jerry's DVD will provide an excellent guide to tuning your 625. However, you have to remember that he has access to a warehouse full of parts that you don't, so he can tune his guns to the Nth degree. With that in mind I would suggest that you NOT try an match his results but set your 625 a bit on the conservative side.
Personally, I've experimented with tuning my 620 for a lighter trigger and it now has an 8 lbs. DA trigger that is perfectly reliable with Speer, Winchester, Remington, and Federal ammunitions.
The final recipe was actually pretty simple. I've handmade shims that fit under the strain screw that allowed me to use the factory mainspring and step the tension down as I tested for reliable ignition. Total shim installed currently is 0.022 inch. I've also installed a 13 lbs. rebound spring after smoothing the frame recess and the rebound slide. Finally, I shimed the trigger by 0.002 inch with a handmade shim on the trigger stud because it was rubbing in the frame recess. BTW, diamond burrs and a Dremel make for pretty quick work of shaping shim stock into fitted shims but they are easy to lose if you drop them. I'll also note the rebound spring selected was because I wanted the SA trigger to break as near as 3 lbs. as possible and the 620 is the only gun that needed a 13 lbs spring to achieve this, my 67-1, 610-3 needed 14 lbs. rebound springs to hit this SA target.
I'll also note that I tried a 12 lbs. rebound spring in the 610-3 at one point and while the trigger reset perfectly in testing it locked up the lockwork twice during live fire testing. If you go too light on the rebound spring, do NOT rely on snap caps to test it, shoot it and see what happens then. I'll also note that the lockup was a bit complex, simply pushing the trigger forward didn't free it up. I had to wiggle the hammer slightly while pushing the trigger forward until it "snicked" and freed up. Bottomline, do NOT go under 14 lbs. with the rebound spring until you've fully smoothed the area for the rebound slide and smoothed the slide completely. I suspect that the pushrod on the trigger came unseated from the rebound slide and that's what tied up my lockwork.
The final aspect of tuning the 620 was to install a Cylinder & Slide extended firing pin. This firing pin features both a slightly longer overall lenth as well as a longer travel slot than the factory firing pin. I tried one in my 610-3 when the mainspring was still at full factory power and based on my experience I do not recomend the installation of this firing pin until the DA trigger has been reduced to 9 lbs. or less. With the mainspring at full power the primer strike was hard enough that it fractured a full 30% of the primers, which was quite obvious when I was putting my fired casings back into the ammo trays for storage. Thirty of 100 rounds showed dark primers and microscopic examination of those primers showed that every one had microscopic cracks in the dimples. Now that I've tuned the trigger in the 610-3 to 9 lbs., I've not seen one single dark primer.
Now, some final notes.
During all this experimenting I've been testing both DA and SA shooting. Ammo used for the DA testing was all Speer due to it's reputation for "hard" primers and SA testing was with Amercan Eagle because it's cheaper and easier to find. The SA shooting has been done from a benchrest at 35 yards using a reflex sight. When I first took the 620 to 8.0 lbs. I noticed that my shots were stringing vertically. At first I thought this was due to variation in the cheap American Eagle ammo I was shooting for the SA testing. However, after doing a bit of fishing on the Net I found that primers can suffer from incomplete ignition with a "marginal" strike. Meaning, it may go bang but it's a fizzy bang that doesn't ignite the powder well. The result is vertical stringing due to incomplete ignition and varations in velocity. Installing the extended firing pin resolved this issue. BTW, I recently tried the 620 out with a scope mounted at 50 yards and shot a 4 round 7/8 inch group with 3 or the 4 in a 1/2 inch cloverleaf, so I am seeing superb accuracy after all this tuning.
Second, my reading on the net also has led me to believe that Primer Ignition is the result of the transfer of Kinetic Energy and NOT Momentum. If you remember your high school Physics, Kenetic Energy is a result of Velocity Squared times the Mass, Momemtum is Velocity times Mass. This means that a lighter hammer moving faster will produce a more complete primer ignition cycle than a heavier hammer moving slower. Basically, I believe that you can tune a gun equipped with a Service hammer lighter than you can tune a gun with the wider Target hammer. It also means that a Bobbed hammer can be tuned lighter than a Service hammer. Yeah, this does go against intuition, however it is quite predictable if you have any familiarity with Newtonian Physics and I believe this to be true. Quite simply, lighter hammers allow you to tune for a lighter DA trigger pull. In addition, a lighter hammer will produce a faster "lock time" which can matter when you are shooting for pinpoint accuracy at long range.
BTW, this knowledge has me constantly doing "thought" experiments about how to construct a Carbon Fibre or Titanium superlight hammer, unfortunately I have not yet had any success in figuring out how to bond a steel sear to either Carbon Fibre or Titanium. One of these days I may actually order up some Titanium and use the CnC gear at work to make a DA only hammer for the 620 out of that light material just to see how light a DA trigger can go with a superlight hammer. I have a sneaking hunch that with a needle bearing pivot, a 3 lbs. DA trigger just might be possible.
Bottomline, you can get a much better trigger, all it takes is a bit of work and a bit of experimenting. If you really want to push the limits, I would recomend that you purchase a Lyman digitial trigger gage, they are much easier to use than a spring gage and allow you to proceed in small increments. I'd also suggest that you plan on doing lots of reliability testing to insure good function and accuracy. If you don't want to push the limits, throw in a 14 lbs. rebound spring, tune the DA trigger to 9 lbs. even, add either a C&S or Apex Tactical extended firing pin and call it good.