Bearing load and other stresses increase more than common sense might suggest because the weight of a chuck is proportional to the square of it's radius. A 50mm x 125mm chuck is roughly twice the weight of a 40mm x 100mm chuck, not 25% heavier. And because bigger chucks will used to support heftier work as well, the total stresses could be out of specification.
As even grossly overloaded machines are unlikely to fail immediately, such 'upgrades' often seem harmless. It takes time for damage to become apparent, thus a bearing that would have lasted 20 years, now only lasts 2.
Bodgers rarely think about long term consequences, so in their world this isn't a problem. Think twice about buying a second-hand machine the owner has 'improved' with this sort of modification. Self confidence is not valid engineering, ask to see his sums and references!
But hobby lathes generally have an easy life. They aren't worked flat out round the clock like production kit. So while I wouldn't fit an oversized chuck to a lathe as a permanent feature, I'd happily risk it to get the odd job done. Point is it's a mistake to overload machines all the time, but thay have a safety margin that can be exploited occasionally. Don't take the p*ss though, best get a bigger machine when lots of heavy work is to be done.
Easy test. Put the big chuck on and use it to grip a suitably heavy lump of metal. Then put 360 hours of work on the bearings, gears, belt and motor by leaving the lathe running continuously for 15 days. Would it be a surprise if this caused a problem?
Dave