The larger cylinders will operate at the same pressure as the smaller ones since that is set by the relief valve and/or the pump. There will be no additional strain on the hydraulics other than pumping more fluid which will take longer.
The issue of the resevoir size might be a concern if you are talking a 6-inch cylinder or something, but going from say 2 inches to 2.5 or 3, the resevoir is probably large enough.
If the remainder of the machine is not beefed up as well, it "may" fail in some other way:
1. Tip over if the ballast is not sufficient.
2. Overloaded tires can fail in disasterous ways - imagine if one were to come off the rim on a side slope or something.
3. Bend or break something on the bucket, arms, mount, frame, or front axle. The bucket is probably the cheapest to replace or pound back into shape.
4. There may be clearance issues that are not obvious until you cycle through the entire range of motion.
5. The failure may not be immediate. You may end up stressing portions of the machine beyond its yield point, but not to its ultimate tensile point (bends back and forth, but does not break immediately). Repeating this cycle will eventually lead to stress factures.
6. The slowness may be more annoying and less productive than the lower capacity was.
7. The added wight of the larger cylinders may partially offset the additional capacity. Especially if you also up-size the bucket cylinders.
8. The true destructive power of the larger hydraulics may not be apparant right away. You may think everything is working great until you come up against an "immovable" object.