What weekly goal should I set for weight loss?

One rule of thumb is to lose no more than 1% of your current body weight per week. But even then, it's good to lose less as you get close to goal weight. For example, reduce your loss rate to 1 pound per week at 20-25 pounds from goal, then 0.5 pounds/week at 10 pounds or so to go.

Why? Because your body can only burn a fixed number of calories per pound of fat you still have. IIRC, the number is 30-something calories. If your calorie deficit is greater than (30-something calories X number of fat pounds remaining), your body will burn some other kind of tissue, like . . . say . . . muscle. Don't want that.

Quick loss has some down-sides. Besides potential for losing lean body tissue (like muscle) if your deficit is too high, it may increase your risk for long-term "adaptive thermogenesis". What does that mean? You could end up burning hundreds fewer calories every day, for a long time, maybe permanently, even after you reach goal weight, compared to someone who weighs the same but never lost weight. Which means you'd have to eat less, maybe forever, to stay at goal weight. Not fun.

Personally, I tried to lose around 2 pounds a week until I got to 20-30 pounds from goal, then tried for 1 pound a week. When I got 10-15 pounds from goal, I added calories to lose at around 0.5 pounds a week. When almost at goal, I kept adding 100 or so daily calories every week or two, until my weight stabilized near the bottom of my goal weight range (which is 120 plus or minus 3). 60+ pounds of weight loss took 10-11 months, which seemed plenty fast enough to me.

I recommend starting at 1lb a week to see how hungry you are and how your energy is. If it's pretty easy to stick to that, bump it up to 1.5 and if that is not too difficult either, bump it up to 2lbs. By starting low, you will be less likely to cheat or get discouraged.
Think of how long it took you get into the shape you are in now; it only makes sense that it will take time to reverse that. Baby steps are best and consistency is the most important consideration.
FWIW, I'm maintaining now but, when I was losing, I managed 1.5lbs a week without too much suffering.
Good luck to you!

I've set my goal at 2lbs a week, nor do I eat back any of my exercise calories (walking). I think it gives me wiggle room if I go over or estimate my calories wrong (I don't weigh and measure my food yet).

I will reconsider if I get tired or too hungry tho.