VJJK: I would most certainly encourage you to keep exercising, including resistance training of some kind. What form that takes is entirely up to you, but there simply isn’t data to suggest HH enlarges at any different rate in lifters vs. nonlifters. When physicians or others recommend that people with HH stop lifting, they are demonstrating two things: 1) their ignorance of what happens inside the abdominal and thoracic cavities during lifting and 2) the innate conservative CYA attitude of the Healthcare industry at large.
Most doctors are not weight lifters themselves and have only cursory understanding of what is going on. They know there is an association of straining with hernia development in the groin or at the navel and thus assume it must also affect HH. Body wall hernias at the groin or navel are different in nature than HH; they usually are either congenital and grown slowly over many years or are the result of sudden tears in the muscle and fascia at these sites, sometimes caused by lifting but sometimes by even innocuous activities. Straining frequently can certainly make inguinal or umbilical hernias grow over time, largely because there is no opposing counterpressure pushing back against that point of weakness in the body wall.
The impact of straining on HH growth, however, is more theoretical. COULD constant straining and very high intraabdominal pressures (IAP) increase HH size? Possibly, if done while still breathing regularly; but very unlikely because its hard to lift heavy and breathe totally normally at the same time. We innately Valsalva to help stabilize ourselves during heavy lifts. The reason I told you unlikely in my first reply is because for there to be a significant upward force on the stomach, pushing it out of the abdominal cavity and up into the chest (which would create HH growth), there would have to be increased pressure from below the diaphragm (elevated IAP) without any matching increased pressure from above (intrathoracic pressure, ITP). This is not what occurs during a Valsalva, which is performed while holding one’s breath. By closing the airway, we increase thoracic pressure significantly and this pushes down against the diaphragm. It counteracts the pressure caused by core muscle contraction of the abdominal wall during a strained lift. IAP does typically rise above ITP, but the difference is small and I don’t think that difference is enough pressure to actually make the HH grow (this part is just my opinion, I don’t know exactly how much pressure differential is needed in short microbursts to stimulate HH growth over time, and that’s why I say unlikely rather than simply no way). There is no large pressure differential across the diaphragm, so that obviates the purported mechanism by which heavy lifting would make the HH expand. These Valsalva events during weightlifting are also usually very short duration, a few seconds at most. That is not the kind of pressure currently believed to cause stretching of the connective tissues around the diaphragmatic crura, through which the lower esophagus passes and that have to stretch in order to allow the HH to expand. That kind so stretching is a very slow process in response to constant elevated pressures, most commonly by an obese abdomen creating constant upward pressure against the diaphragm, especially while supine, and/or by frequent gastric distention with large meals. This is why we counsel HH patients to eat numerous smaller meals through the day rather than a few large meals.
You may find this article useful: Systematic review of intra-abdominal and intrathoracic pressures initiated by the Valsalva manoeuvre during high-intensity resistance exercises - PMC. Of note, if you do choose to continue weight lifting, there does appear to be a larger pressure differential across the diaphragm in some movements, such as the leg press, while in others, such as the bench press, there is almost no difference at all. In fact, you create more pressure differential by coughing or sneezing than you do in most weight lifting. So, on balance, I would personally consider the health benefits of weight lifting to outstrip and justify whatever risks might also be present when lifting.
Hope that is helpful.