Apparently, they do. For example, the white-tailed deer has a shoulder height of 1.0m to 1.1m, and that's in the North. Towards the South, they get smaller.
I guess, that would be a general thing. Mainland US is relatively temperate. The real giant kinds of deer, like e.g. moose/elks, only really live in colder regions, which are further north (including in Alaska).
I worked at McDonald's for quite a while as a teen. A regular hamburger patty there is 1/10 lb and a quarter pounder is...as you might suspect 1/4 lb. That would make an adult deer weight between 80 - 200 lbs.
The average weight of an adult male whitetail deer is 203 lb (maximum, 405 lb). The average weight of a female is about 155 lb (maximum, 218 lb).
I don't recall receiving any training on the weight of the condiments or buns, but I'd suspect they weight slightly more than the small patty amd slightly less than the larger one, so let's assume 1/5 lb. That changes our original 80 - 200 lb range to be 240 - 360 which is a little too heavy.
In conclusion, hamburgers are a shit measurement, but if you had a mix of 800 child-size and adult-sized burgers and you hit it with your truck, it would do a similar amount of damage as hitting a deer.
Yeah, it's particularly weird, because surely people from the US have a good sense how much a pound weighs, and a pound weighs more than a burger, so you need to imagine a less big number of them.