I think the idea "Cessna put bigger engines in the C-172 as bigger engines were certified" is a bit simplistic.
Compare an early model Skyhawk to a late model - they have very different empty weights, which is reflective of how the basic design got heavier over time. Electric flaps, g-rated seats, seatbelts (and now airbags), more avionics, different wing shape, a vacuum system, big square dash, new landing gear - the newer ones are very different aircraft. You can tell if you fly in them too, the older ones are not underpowered at all, if they're not overloaded. A new 172 with G1000 weighs over 300lbs more empty than a 1956 model did, yet the 1956 model has a bigger useful load despite having 35 fewer HP.
Here is some data I pulled from the 1956 model handbook vs the S (G1000) model POH:
Model Max Weight Empty Wt Useful Load HP Wing Ld Climb Takeoff Gnd Roll
1956 2,200.00 1290 910.00 145 13.8 660 1650 725
P/G1000 2,550.00 1663 887.00 180 14.7 729 1186 693
Takeoff distance is to 50', performance all assumes max gross wt. sea level, no wind, 15C.
I think it is especially important to look at the useful loads here. If Cessna were upgrading the engine because "we're getting fatter" they would have increased the useful load. Instead, the engines evolved over time - as did the airframe and equipment - as one cohesive design, while useful load stayed more or less the same (actually, it went down slightly). It is a back and forth related to technology (1956 vs 2010!), and the additional engine power really is just enough to keep the design competitive (power to weight ratio on the 1957 model is 0.066 vs 0.0707 on the current model, which is part of why the distance over a 50' obstacle is so different, but the other numbers (ground roll, sea level climb) are fairly similar.). In fact, I would suggest that an early 172 and a late-model both feel "underpowered" compared to a mid-70s N-model, when the design was still light but the engine made 160 HP. With a power to weight ratio of 0.070 and a wing loading of 13.2, it climbs at 770 fpm at sea level, better than either of the other two.