Firstly, good on you for being concerned about her and asking about it on a public forum where others who may not be able to can hopefully benefit from this as well. I hope you come back with your findings from the airlines/trips they take!
Basically, it comes down to the airline. You can see what their policy is by looking up their Conditions of Carriage. Very few do specify exactly something about weight/height/size, but will merely talk about 'a passenger's physical state causing discomfort to other passengers or crew', which is more likely to be used against those intoxicated, or if you tried to board while say, covered in manure??
A friend just came back on a flight from Honololu to Auckland with Air New Zealand (see related query on Travel.SE), and the person next to them was physically unable to fit into a chair with the armrest down. As a result, all three in the row were forced to endure an awkward and uncomfortable 12 hour flight. Air New Zealand's conditions of carriage only mention 'physical state', but at the time we looked around and found airlines like Southwest in the US are starting to actually mention size/weight in their conditions of carriage.
Your best bet is probably to look up the conditions of carriage, and if it's a little ambiguous, tweet or email the airline and ask them directly. If you have a statement from them in writing saying that there's no problem, that's a very easy document to have your folks print out and take along, just in case there's a problem. If there's not, no embarrassment, it just stays in their bag and they get to tell you there was never anything to worry about ;)
An update, I had a flight a few months back with Qantas, where I was wedged between two very large women. The one on my left was big enough that the food tray couldn't be lowered, and she couldn't locate her own headphone jack in her seat. I found at the end of the flight her similar-sized husband was a row back, because the two of them physically couldn't sit next to each other on the same flight.
It was, as you might imagine, uncomfortable. I spoke with Qantas afterwards about their policies, which they were a bit evasive about, but tried the line "we can't tell how big passengers are until they arrive at checkin". I pointed out that the same applies to my baggage, but they have a size limit on that :/
Their current policy seems to be that if they can, they'll move the inconvenienced passengers, but if it's a full flight, tough luck, and IF you complain enough, you'll get a token appreciation in frequent flyer miles, which is a shame.