My shoe size is about the same as yours, but that has nothing to do with whether to wear a boot or not. Traditionally, people have worn boots to support carrying a large pack or to prevent rolling an ankle. However, like others have said, once you get your pack weight down, there's no reason for anybody of any size or shoe size to wear a heavey boot.
Besides the excessive weight on your foot, despite the popular misconception that boots are great once they are "broken in," in reality, I think your foot breaks down to conform to the boot and not the other way aroound. This can also exacerbate or cause injuries to your feet, legs and back,
If you're using a boot because you need ankle support, you might try some ankle-strengthening exercises instead.
But all that aside, if you're still dead set on continuing to wear a boot, I would opt for one that is as lightweight as possible. You might even try an ankle high hiking shoe as an option.