I have about 3 acres to mow, and all that I can afford is the one that's rated up to 2 acres. It's a John Deere ZTR 355R. This may seem like a stupid question, but you see on everything, take 2, and Grandma says 4 is fine. Terrible example I know... but realistically, what stress/risk am I placing on a mower by pushing it beyond it's "rated" specs? I inquired with Deere but they stuck to the book.
That's not a specification. It's a buyer's guide statement, written by the marketing flacks, to at best help guide you to the right unit for you. You certainly don't need to follow it to the letter.
It probably factors for things like mowing speed (how long will your mow sessions last), bag capacity (how often must you go to the compost pile to dump), etc.
Presumably the manufacturer gets to see a lot of detail about where their machines do well and the reason they may require a lot of attention. My guess is that based on experience they are trying to guide your purchasing decision. If this is right then you could expect the lighter mower to cut grass just fine if more slowly, however it might be wise to expect more maintenance. Pay close attention to the ease of replacing belts, starter motors, coil, oil change, blade maintenance, cost and availability of parts and so on. Consider that for a heavier machine that requires 1 hour maintenance for 10 hours cutting, the lighter one might need 2 hours, so it becomes a matter of your time and the value you place on it. If someone else does your maintenance, assess how easy it would be to transport the machine to get it fixed.
Simply marketing gibberish. Somewhat based on time it will take to mow (.vs. whatever the marketing department thinks you should be allocating for time to mow), mostly based on separating you from your money. More acres means you have more money means we want to take more money from you....
i.e. you can mow 3 acres with a 20" wide manual push mower. It will take you a while, but it can handle all sorts of detailed edge work that a 72" wide hydrostatic ride-on wondermower won't, and it won't sink into wet spots to the point that you need a tow truck to pull you out - I've seen some UGLY situations with overweight hydrostatic ride-ons and wet ground. It also is going to cost you a HECK of a lot less to buy and maintain.
Actually, my first pesky question with "gargantuan lawn-mowing needs" tends to be "why?" - are you maintaining an athletic playing field for your kids/neighborhood?, or simply mowing a lot of grass because you can't think of anything better to do with 3 acres of land than grow a crop you have no use for on it that takes lots of maintenance? Keeping the grass down between your orchard trees? Mowing off the weeds your cows won't eat? Private mini-golf course?
There are lots of things other than 2-4 inch grass you can do with 3 acres, and many of them are less work/time and less expense, as well as more friendly to bees and other wildlife. Or more useful to you, directly (but don't kid yourself that 3 acres of vegetable garden will be less work - it will, however, be a lot more useful than what use most people put 3 acres of lawn to, and can save or make money. As could 1/2 acre of garden and growing mulch/green manure crops on the other 2.5 acres. Perhaps between the orchard trees...)