First, the following is based on the assumtion that you are refering to a NEW 625 JM and you are the original owner. Keep this in mind, if you have an older 625 with a hammer mounted firing pin some of my suggestions will NOT apply.
One concern about this assumption is that reported 2.5 lbs. SA trigger pull, that it way low for a factory new S&W and in a brand new gun indicates that the sear on the trigger is NOT correct for a factory trigger. If this is a brand new 625 I would suggest that you return it for warranty service. When I recieved my 625 JM at the end of August the SA break measured at exactly 4.5 lbs., as did my 620 and 610-3.
If you purchased the gun used it means one of two things. One is that the previous owner has ground on the single action sear on the trigger. Second is that a previous owner has installed a 12 lbs. rebound spring. If you have another revolver you can use for comparison, compare the tension on the trigger AFTER the hammer has dropped, if it feels obviously lighter you have a light rebound spring installed. If the tension of the trigger after the hammer fall feels the same on both revolvers, odds are the sear on the 625 has been reshaped to reduce the SA weight. I do NOT advise changing the SA sear on the trigger from the factory angle because I believe that it can lead to Pushoff by increasing the rate of wear on the tip of the SA sear on the hammer. IMO a much better approach to reducing the SA trigger break is to install a lighter rebound spring. Personally, with a factory trigger I prefer a 14 lbs. rebound spring because it will produce a SA break of 3 lbs. which is just where I like my SA trigger to break. I've also found that a 14 lbs. rebound spring will provide a good rapid trigger return.
Now to the heart of the matter, that 14 lbs. DA trigger. That is a bit on the heavy side for a brand new S&W but NOT out of the realm of possibility, S&W has been shipping revolvers with heavy DA triggers for at least the past 5 years. My 620, 610-3, and 625 JM all had DA triggers that measured between 11 and 12 lbs. when new. They do not need to be this heavy but I suspect it's being done due to liability concerns.
Step one is a good cleaning, while all 3 of mine came with the internals clean I've seen some sporadic reports of new gun with debris in the lockwork.
Step two is proper lubrication. All 3 of my newer revolvers were nearly bone dry when new. Personally, I like a small dab of RIG universal grease on the hammer and trigger pivots, a bit more under the rebound slide, and small drops of premium oil on the sear, hand, and cylinder stop. BTW, for me premium oil is 5W30 Mobil One.
Third step is adjusting the mainspring tension. I do mine by installing a hand made shim under the head of the strain screw. Using shims allows my to dial in the DA trigger weight to the exact value I want to achieve. Other options are to file the tip of the strain screw (have spares on hand if you do this) or to use locktight on the strain screw to hold it in position when backed out slightly. Personally, I regard locktite as a temporary solution because in time I belive that the strain screw will work loose and lead to misfires. BTW, just for reference, installing 0.030 inch of shim under the head of the strain screw on my 625 JM reduced the DA trigger from 12 lbs. to 8 lbs., so you don't have to move the strain screw much to have a large effect.
Now, how light do you want that DA trigger? If you want to take it down to 8 lbs. you'll need to take some steps in insure reliable ignition and you'll need a truly accurate way to measure the weight of the trigger. BTW, I tried using fish scales, they were neither repeatable or accurate for me. I now use a Lyman Digital and it's proven both accurate and very repeatable. In addition, for those guns that feature a hammer mounted firing pin I cannot assure that you'll get reliable ignition with a DA trigger at 8 lbs., the frame mounted firing pins offer options that are not available with a hammer mounted firing pin. With a hammer mounted firing pin, I stop once the DA trigger weight hits 9 lbs.
Now, specific approaches and recomendations. If you have a frame mounted firing pin and want to stay with the factory firing pin, you will want to pull the firing pin and measure it's overall length. S&W has increased the length of the firing pins recently and an older "short" firing pin will NOT allow you to take the DA trigger as light as you can with the more recent "long" firing pin. BTW, the firing pins delivered in my 2008 620 and 2009 610-3 measured at 0.480 inch overall length, the firing pin in my 2011 625 JM measured at 0.491 inch. If you have a 0.480 inch firing pin I recomend running the DA trigger at 10 lbs. even, any lighter and you may have misfire issues with some brands of ammo. If it measures at 0.490-0.495 inch, I believe that you can safely take the DA trigger down to 9 lbs., however you may have misfire issues when shooting without moon clips.
If you want to take the DA trigger under 9 lbs. you will have to install an aftermarket firing pin.
I've used a firing pin from Cylinder & Slide in my 620, 610-3, and 625 JM and they word quite well, however because they are not only longer but also feature an extended travel you must NOT install this firing pin until the DA trigger has been reduced to 9 lbs. or less. If you install this firing pin in a revolver with a heavier trigger you run a very real risk that it may pierce the primer and get stuck there and that won't be easy to fix. However, I can report that this firing pin works perfectly with an 8 lbs. DA trigger and with or without clips my 625 JM will ignite every brand of ammunition I've been able to find.
Apex Tactical also offers 2 aftermarket firing pin options. First is a 0.495 OAL firing pin. Second is a 0.500 inch XT firing pin. When I purchased my 625 JM I had planned on trying the 0.500 inch XT firing pin because I suspect that XT may refer to extended travel, however it was out of stock so I went with the C&S firing pin. About all I can report is that Apex has a very good reputation and it's likely well deserved.
Now, one caution about any long or extended travel firing pins, that is using snap caps is a MUST. Cylinder and Slide specifically states that snap caps must ALWAYS be used for dry firing and there have been reports they will "wad up" the firing pin return spring if you don't use snap caps.
Finally, as an example of the differences between the C&S firing pin and the factory firing pin I've attached a drawing showing the measurements I took on both.