I'd just like to say one thing : you need to do it for YOU

My boyfriend is neutral. He does not provide support and neither does he put me down. If he notices I look smaller he compliments me, and he nods if I tell him about my workout/weight-loss/etc, but unless I look for it I usually get nothing.

I've learned that you need to be doing this for yourself only. It may sound selfish in a way, but this needs to be your main motivation. It may hurt that he is unsupportive, but use this to make yourself stronger, say you will prove him wrong and shrug off his negativity.

Adding: Considering he is pretty overweight, as you say, I think he needs to keep his pie-hole shut. It's not like he is s skinny mini with a 6 pack. If my boyfriend was overweight and said something about how I looked, I would tell him to take a look at himself instead of criticizing others.