Hey, that’s just efficiency. Bullets run a lot faster than any cop I’ve ever met. 
Most of your examples (first and third) are Texas Dept. of Public Safety State Troopers. That cowboy hat and western-ish outfit is their official uniform.
For counter-examples of Texas cops that don’t look hillbilly-ish, here you go:
Houston Cops
More Houston copsDallas cops
One thing to remember is that a LOT of US cops wear lightweight body armor when on patrol, and this makes them have a more… rotund look than they probably really have. I’m guessing that’s what’s going on with the women cops in the last photo.
Plus… if anything, US cops are prone to looking too martial, instead of too hillbilly, I’d say.
And then finally, there’sthis European cop to provide a counterpoint…
Don’t forget this one…
http://uploads.tapatalk-cdn.com/20160610/44b2a0514d33359ec058262e963a1b5b.jpg
What’s the deal with all the blind cops in the US?
And you just watch your step in this part of nath Caralina.
I sat in a pedestrian mall in Darwin, and watched Australian cops dispersing a group of aborigines, and I was struck by how amazingly they looked like Ameriacn cops or deputy sheriffs, way overweight with the same swagger and brush-cut.
Reno cop. Not hillbilly. A bit white trash maybe. 
I’ll make a sweeping generalization and say that European people in general are thinner than American people in general. And by definitely less hillbilly.
Why is that? Is it culture? They like to eats lots? Like to eat 4 times a day? Like to have lot of junk food or fast food all the time?
It is no mystery that most Americans are overweight that the culture will not snowball onto the police.
UK may be not so bad like the US but they are starting to get overweight the people and the police in the UK. If you take out European people out side of UK people they are lot smaller.
Every European I talk to they are really shocked at the amount of food we put on the plate.
You go to a fast food place in the US you can easy take in 600 calories or more. You go to say McDonald’s and have big mac and the drinks and dessert that well over 1,000 calories.
Some people may not get any where close to that amount of calories adding breakfast and lunch on a normal diet size. That you eat at one go at McDonalds.
One plate serving can easy be two plate servings in Europe eating at two different times in day. If you eat you normal three times day.
If they are eating 600 or 1,000 calories per meal that is lot of calories. If they eat 3 to 4 times a day. Even 2 times a day it is lot of calories.
Fat people! Amirite?
Former Arlington Texas police officer:
There was web site showing the most and least fat people by city. I will have to find it but Dallas and Houston was high on the list.
By nation what is it one in three are overweight?
Why don’t you just roll with more officers to Hot calls than bulking up or use the taser or get some MMA training? If you get bar fight, street fight or a family violence call with some drunks fighting. Send 4 or 5 officers than two big officers?
Unless we’re talking tightie whities here, how do your balls not fall out of shorts like that? Inquiring minds.
And I like how are OP does selective answering. That’s cute.
Actually there was only like one fat cop in two of the pictures the OP posted and a lot of lean cops in the pictures too. In a society and increasingly a world where obesity is becoming obese its not surprising. Add on that people who sit in a car a lot of the time, get fast food a lot for convenience sake, and often work night shifts which fucks with the body’s natural circadian rhythm and contributes to obesity its not really a surprise.
Not sure about the hillbilly thing, what are your parameters for hillbilly? Lumpy white guy held together by doughnut batter?
that’s a pic of Tom Lennon, playing “Officer Jim Dangle” on the show Reno 911. The shorts were basically part of the joke.
Economics 101.
And I see my joke fell flat. Gah.
But yah, I know. I’ll try harder at this funny thing next time.
Hee. Chicken-fried lumpy white guy works too.