I own a Specialized Secteur Elite. Currently I ride on 700x25c both front and rear. I weigh around 240 lbs. I inflate my rear tire to 125 psi (max on the sidewall). According to the famous 15% drop chart this isn't enough. Should I change the rear tire to 700x28c? I don't get any pinch flats with the current setup.

They why mess with something that's working? Also, You might try backing off the tire pressure a bit. Maybe 115-120 to start. I'm 200lbs and frequently ride closer to 90psi. I'm not sure what chart you are referencing, but every formula I've tried had me at a higher pressure than I was already using successfully.

The bike may not have room to fit a 700 X 28

There is room for 700x28c, if I've done my research correctly.

The chart I'm referring to is this one: https://www.bikequarterly.com/images/TireDrop.pdf

Get one and try it.
I have a 700 X 28 Michelin tire that measures as 30 when on the rim.

If you're not getting pinch flats now then no need to change. However, you might find you like 28s.

Thanks for the answers so far. Since you don't think it's necessary, maybe I'll try it when it's time to change the rear tire. Or if I find a spare 28 for free...

At 237# (4 months ago & before) I found the venerable Continental GP4000 700x25 tires worked well. Lots of miles, zero flats until the sidewall failed. I run about 100 PSI up front and 115 in the rear. Unfortunately ProBikeKit.com is out, but that's the place to buy them (delivery takes 5-7 days, IIRC).
Good luck.

I have bikes with 25mm, 28mm, and 32mm.
My favorite is the 28mm, and I do use the 15% drop method for inflation pressure.
I weigh 185#.
And btw a 28mm Gatorskin on a 23mm rim actually measures 27mm.

Interesting. IIRC, someone else recently reported a 25mm Michelin measured 27mm.

Imho, those charts are rough guides at best. We run 25mm tires on the tandem with a team weight of 350lbs at 110-115 psi with no problems, which is way off what the chart would suggest.

Sounds right to me. I use Mich and Conti tires in both 23 & 25mm and the Michelins are always visibly larger on the same rim and PSI. Noticeable when putting wheels on and off.

I rode a set of 28 for the first several years after returning to cycling. I was new back to the sport, and with the "newly" acquired prosthesis, didn't want to take any chances with flats of any kind. I used a set of hard case tires, which I am sure had some impact on the feel, and turning was very slow and cumbersome feeling compared to the 23 that came on, and that I later switched back to.
With that said, I NEVER had a flat with those tires of any kind.

I am a 210~#, and have weighed considerably more. I swapped back to 23 Conti's, run them at about 100PSI and have had no out of the ordinary issues with them as far as tire or rim are concerned. If you aren't having issue now (but second the idea that you lower pressure some) then I don't suspect you have any real reason to change to a larger tire unless you just want to.

am running the rubino pro 28s on my caad9 right now, i love 'em, takes the edge off the stiff aluminum nicely. won't fit a lot of bikes. a lot less cuts than the michelin pro race 2 and 3 that i've run for years. not as nice as the vittoria open cx but then what is?

why does everyone overthink all the little stuff? it's only a relatively inexpensive set of tires, if you know they fit, buy'em and try 'em and decide for yourself, if you don't like them buy something else and put them on the shelf as spares

Overthinking little stuff? U know this little stuff costs 50 bucks, right? I'm a student and I don't have any income on my own...