Anti discrimination laws eliminated the use of height and weight requirements. Most departments have strength, stamina, and agility requirements. There are minimum requirements to get hired and higher standards to get through the academy.
A 300 pounder would have to run the same distance in the same maximum time as a 150 pounder. A 105 pound woman would have to do the same minimum number of pushups as a 160 pound man. Many people are weeded out through this process.
A few decades ago, while working as a plaster room attendant in a busy hospital in a very conservative midwest city, a cop brought in a patient. The cop had to weigh a minimum of 300 pounds (probably 100 of that was fat) and was no taller than 5'8". In addition to that he had to have at least 10-15 pounds of stuff on his belt. (357 magnum, extra ammo, handcuffs, mace (before the days of pepper spray), a big jangly bunch of keys, walkie talkie)
I didn't want to ask if he actually could run the 100 yard dash (again, before meters), but I just had to ask, "When you run your annual physical fitness test, do you have to do it in uniform and wearing all that stuff on your belt?"
"I don't run," he announced in a deadpan voice.
Confused, I asked, "Do you mean you don't have a physical fitness test? I thought all police and firemen had that."
"I don't run," he repeated.
More confused, I asked, "What if there's a criminal running away from you?"
The cop replied calmly, "If he did something that I can shoot him for, then I shoot him. If not, then he gets away."