Right off the bat, while there are baselines for different cultures, the most important thing to remember here is that your relationship is, first and foremost, a connection between two individual people, and those people both need to be happy, regardless of whatever the mainstream standards of their individual cultures are.
Getting to your specific questions/comments:
uAre weight comments acceptable in Japan?v
I think it'd be oversimplifying things to just say "Yes, weight comments are acceptable in Japan." But compared to the U.S., yes, people in Japan are more likely to openly comment on a person's weight.
I've seen Japanese people comment on my foreign friends' weight, in front of them, several times, but rarely, if ever, in an insulting tone. Instead, they've been very matter-of-fact statements, along the lines of "Oh, Bob, since you're fat you must think the portions at restaurants in Japan are very small, right?"
While this kind of comment definitely isn't a compliment, often it doesn't seem to be intended as an insult either, but just as an observation. So the question becomes why this "observation" is comparatively more accepted in Japan than in the U.S., and I think a huge reason is that Japan and the U.S. have different opinions about what causes obesity.
In the U.S., especially over the past 30 years, obesity is largely seen, or at least treated in polite conversation, as a result of outside influences. "That person is overweight because they eat a lot of high-calorie fast food, but they're in an economic class where fast food is their only option." "That person is overweight because they have a lot of stress from an unhappy family life, and eating is their way of coping with their emotional pain." "That person is overweight because the local government doesn't invest enough in green spaces with public exercise equipment."
In Japan, however, obesity is primarily seen as a result of an individual's chosen lifestyle. "That person is overweight because they eat a lot/a lot of junk food, and/or they don't exercise very much." Add in the fact that the traditional Japanese diet (rice, fish, vegetables) is very low-calorie, plus that a lot of time at least walking every day is built into most public-transportation dependent lifestyles, and the concept of "this person is overweight because of the unbalanced lifestyle choices they make" becomes even stronger.
Put more succinctly, in the U.S., the idea is usually "this person ended up overweight, so I should avoid the delicate topic," whereas in Japan it's more often "this person chose to be overweight, so there's no need to act like they aren't."
Of course, there's an additional wrinkle that being overweight generally isn't considered an attractive/positive trait. But, as an example, let's say someone had a green mohawk, or an unwashed beard that stretched down to your knees. Those are also things that most people would consider unattractive, but they wouldn't feel the need to avoid commenting on them, because they're choices that person made, and often that seems to be how Japan sees weight as well.
Whether or not this makes it OK for your boyfriend to say the things he does about your weight, or whether the average Japanese person would say the same things, isn't something I can say, however,