Your Byetta is good for about 5 hours and peaks at 1 to 2 hours after you take it. This is as it should be as it is there to help ameliorate your food spike. Most of us that are type 2's will rise overnight, mostly due to that pesky dawn phenomenon.
What has me concerned about your numbers is that they are "ok" for a "diabetic", but with whats available for meds and particularly for being a Byetta user, they should be lower. Before you go to bed you should be sub 100 and in the morning you should be around 100 and most definately sub 120. Ask your doctor about adding a sulfonylurea like glipizide or glyburide to your meds mix. This gives your Byetta and extra "kick" and should push your numbers considerably lower. Also try to go for a week with conciously limiting your carbs from starches like potatoes, rice, breads, etc. and see what effects that has on your readings. I know that if I have a hamburger and a couple of fries, the bread and the tiny bit of potatoes keeps my BS around 100 two hours after eating with my Byetta. If I have a steak and a salad, the same amount of meds can leave me at 60, so food can be a major contributor in where you are at for your readings. Hope this helps.