Folks with normal metabolisms, normal thyroids, healthy weights and lifestyles don't have to be concerned with all the little fine points of the chemistry and metabolic set points that someone that is hyper or hypo does.
Even if you are on optimal dosing of your meds, you still don't have the freedom and fail safes that a 'normal' person does. It's up to you to learn what your body needs to help it reach it's healthy weight.
It's up to you to determine what your body needs help with to get back to a healthy weight.
I should make a comment about healthy weight... First, throw away those stupid charts that say if you are this tall, at this age you should weight this much... that is ridiculous. How heavy are your bones? How much muscle mass do you have? What is your BMI? Is your mineral balance out of whack causing you to retain water? All those things should be factored in when determining what YOU should weight. Not those stupid charts.
I, for example, when I weigh what I'm 'supposed' to, look like a walking skeleton. My bones jut out and I'm sick all the time. Put another 40 pounds on me and I'm healthy and happy with good muscle over a strong bone structure, the person that I am is large.. just because I'm large does not mean that I have to become a skeleton to be 'normal'.
Am I implying that being fat is good? No.
Am I implying that being thin is bad? No.
I'm saying that you should aim to be a weight that is healthy for you, be it feather light or well anchored, each of us has a distinct body type that we are and that should be our goal, health, not the cover of a magazine.
Now, with that in mind you have to take into consideration who you are, your lifestyle, habits, budget and family... you need to make adjustments so that the changes you do make not only will help you achieve your goal of a healthy weight but to fit in with the rest of your life as well.
For some it is low carb, for some it's raw foods, for some it's mini-meals, for some it's strictly restricting calories, but for no one should it ever be starvation or deprivation, you simply need to learn what your body needs to be healthy. You've changed, your thyroid isn't working like it did... you have to learn your new body.
That means a bit of trial and error... you're gonna fail a few times.. just plan on it and you won't be disappointed. If one way doesn't work, tweak it until it does or try something else. There is no hard and fast rule to lose weight when you are hypo because how it effects us as individuals is so very different from person to person... but there are some VERY interesting theories and learning them and combining that information with what you know about you and your new body, may get you on the right track to a healthy weight and maintaining it.