I've been training for a half marathon in March, however for the last week I've not been able to do any exercise at all due to having a really bad chest infection. Will missing one week make a lot of difference to my overall fitness and weight?
I am already a very healthy person I'm just concerned it will take me a while to get back into it.
No. Your body can recover. If you were ill then to train on top of that could push you back further. So just agree with all the others who have said this.
Take off the week. Your health is more important than your fitness. And one week won't make any difference. In my experience, distance running is more about mental stamina than physical. Your legs might know that they can do it, but it's your mind that pushes you.
I've had to take the last 2 weeks off from working out (also long distance running) because I injured both my arms and don't think I'll be able to run again for another week or two. I know once I get back into it, my body will be able to do it, but my mind will need the push.