"Think over" sounds as if someone is weighing a decision. Do I do it (something) or not? Which option do I choose? "Think (it) through" means to think about something until you understand it.

Through means going from beginning to end - you go through a thinking "tunnel" until you come out into the light on the other side. Thinking something over has a slightly different meaning - someone might tell you to think it over if they want you to consider something carefully and come back to them later with a decision. For example: Son: I made a mistake because I didn't think it through properly when I applied for my job. I didn't consider the driving involved or how I would feel doing admin work. I've decided I don't want the job after all. I'm sorry, but I am handing in my notice. Mum: Hey, you are making a hasty decision. Think it over before you hand in your notice. Give it some time, and don't make the decision today. If you are still sure in a week's time, you can make the decision then.

"Over" and "through" do not have the same meaning. If you put your hand "over" a table, you will hold your hand above the table. Your hand will not necessarily even touch the table. You can't put your hand "through" the table without breaking it. Putting your hand through something means forcing it through and emerging out the other side. Likewise with your thoughts. If you think something over, your mind is hovering above it, thinking about it but not necessarily coming to any conclusion. If you think something through, you will analyze it and achieve understanding. So you're not making much of a commitment if you decide to think something over. Thinking it through requires more effort. Same as what Adam said, really, just more words.

"Think (something) over" is used more often to describe a binary decision- yes or no, here or there, etc.