I'm about 192 ready-to-ride. Currently running Specialized Armadillo Elite 22C tires on my Felt. I notice the weight bias to the rear of the bike causes quite a bit more deformation of the rear tire during riding, even at full (125psi) pressure. Is there a problem or reason not to run a bigger 25c tire on the back and the lighter 22c up front? Thanks in advance for any insights.

I'm about 192 ready-to-ride. Currently running Specialized Armadillo Elite 22C tires on my Felt. I notice the weight bias to the rear of the bike causes quite a bit more deformation of the rear tire during riding, even at full (125psi) pressure. Is there a problem or reason not to run a bigger 25c tire on the back and the lighter 22c up front? Thanks in advance for any insights.

There is no reason you can't do that and it's not going to really effect performance much, but might add a mm or so of saddle tilt :D

Personally...I run 25c tires front and rear for everything I do whether training or racing. They actually have lower rolling resistance, give a better ride, but are slightly heavier and slightly less aero than a 22c or 23c tire.

The only time I run 23c tires is on my TT bike.

I really don't think you're going to notice a 3mm diffence.
But, yes, the wider a tire is, the more weight it dispalces
Now if you did a more radical differentail, it may make the handling a bit "twitchy"
MTB's run a wider one up front to for the oposit effect.

been running michelin pro2race 23 up front and 25 out back for while
(over 1500 miles) with no issues. slightly more comfortable ride.
after i ran over a sharp object and totally sliced open a 200 mile old tire,
i replaced it with a conti ultra gator 25; i felt it was a bit squishier(likely
due to the thicker tread) when descending, but not too much difference
in traction, although the RR feels a bit higher than the p2r.

overall i think continue to run 25 out back, primarily for the comfort level.

There's generally no handling issue or other problem. In your case, it might let you run lower pressure in back, increasing comfort and improving handling, with no speed penalty.

They actually have lower rolling resistance

There is no conclusive research to prove this- show me one study that says it does, I will show you 3 studies that show you are wrong.

I'm about 192 ready-to-ride. Currently running Specialized Armadillo Elite 22C tires on my Felt. I notice the weight bias to the rear of the bike causes quite a bit more deformation of the rear tire during riding, even at full (125psi) pressure. Is there a problem or reason not to run a bigger 25c tire on the back and the lighter 22c up front? Thanks in advance for any insights.
The Conti Attack/Force combo is a 23 in rear and 21 or so in front. The fronts wear much slower than the rears so I guess it makes some sense. Didn't like the way a really skinny front handled though. I went back to 23's all around.

That's what I've done for years! As you've noticed, the rearwheel, especially with comfort bikes like the Roubaix, carry more weight than the front. A larger rear tire will give you a better ride, and most importantly, make pinch flats much less likely. I disagree with the previous poster who said you might add slightly to the saddle tilt. Since you are noticing the rear deforming more, if anything, this will level things out. Truthfully, any rider over 200 lbs, and you're pretty close, should run a 25 in back if not front and rear. I think you will be very pleased with the ride difference in a 25. though it may not seem like a significant difference in width, a 25 is also a somewaht taller tire. I think I read somewhere that a 25mm tire has nearly twice the air volume as a 23 mm tire. That's a lot of extra cushion to absorb impacts.