Q: Are oversized eggs that are difficult for my hens to pass caused by overfeeding?
A: It is not likely that the problem is overfeeding. We recommend feeding free choice and not limiting their feed: underfeeding usually causes more problems than offering extra. It is rare for a layer to overeat ("meat" birds like the sickly Cornish Rock crosses are different, and often overeat). If it really concerns you, you might cease fatty treats, or perhaps double check the protein level in your food. Around 16% protein or so is good for layers, so if your protein level is higher than that, you might switch to a slightly lower protein feed.
For the most part, though, egg size is genetically determined and won't be affected very much based on eating a little more or less on certain days. Specific breeds lay large or extra large eggs, while others lay small eggs. The egg size a hen lays has to do with the size of the shell gland and ratio of the length of the magnum (where the albumen is deposited) to the whole length of the oviduct.
It does occasionally happen that a hen may have an egg that is too large for her and get egg bound, but often egg binding can be caused by a deficiency in calcium (causing hypocalcemia or tetany) or phosphorus (which helps with calcium metabolism), not by eating too much. Chickens that don't get enough exercise or that are excessively fat may also have issues with egg binding, so be sure to offer them plenty of space in their run to roam and exercise.
Another thing that can cause issues is simply the fatigue of the muscles associated with laying (or possibly a deficiency in magnesium, which helps these muscles work). This happens when chickens don't get their natural seasonal break or slow down in laying, so be sure to allow your hens to have their natural winter break or slow-down, rather than keep them under artificial light to increase laying during the cold months. Additional problems with large egg size may be caused by nutritional imbalances relating to methionine or linolic acid. Unless you blend your own feeds, this shouldn't be a problem with any commercial brand of feed.
Remember, though, it is quite natural for a hen's eggs to grow larger over time. The first eggs a young pullet lays will be small (by comparison with the average for her breed). They grow larger as her system gets into the swing, and sometimes eggs don't reach their full size until after the first molt. Occasionally a capillary will break as she expels the egg, and in most cases this isn't a problem, although it isn't ideal. If there is a large amount of bleeding, you should be concerned and consult a veterinarian. We are not vets, and can't diagnose the problem. If you do continue to have issues with bleeding, you should consult a vet to get a firm diagnosis and treatment options.