K.H.
Some kids so just like to eat , I was the exact same way and my mom wasn't strict with food and let me eat as an when I wanted , and anything I asked for , so no surprises that I became over weight from around age 7 until around age 18 when I decided to change my eating habits. Don't get me wrong and I am not "skinny". I'm well built and come from a family that are well built but I am not fat anymore , which makes a big difference.
At 16 months it is difficult as she will just scream when she don't get what she wants , as long as you make sure that her meals are healthy and nutritous and she snacks on fruits then she should be ok. Keep her active , either out in the yard running around or take her to the playground , and if you and your husband also eat good foods then she will learn from your eating habits. Of course she is going to want candy , cookies , ice cream etc , everyone does , but this is where it is your job to teach her that yes she can have those things but in moderation.