How to deal with people offended if you don't eat

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I am just about to join a drive from the UK to a Children's rehabilitation centre in the Ukraine to deliver Humanitarian Aid. I will be sharing the driving of a van and trailer with my husband for a charity called UK Aid. (btw, if you would like to help sponsor the costs of the trip, or track the progress, please visit http://www.justgiving.com/Dirtyweekenders-Ukraine-2012). I am really looking forward to the experience, as I have supported the charity for many years, and this will be my first visit to the Ukraine.

My problem is that I have been warned that when we reach the centre, the families and staff will offer us a lot of food, and are actually offended if you refuse. They have so little to give, refusing the food is like turning your nose up at an expensive present.
I've been doing pretty well since I joined mfp earlier in September, and I don't want to lose momentum. They will obviously see that I enjoy my food (I'm currently at 218lbs, so it shows!), and as they don't understand much English, I'm not sure I will be able to explain properly to them.

I don't want to offend anyone, but I don't want to go back to bad eating either. Any ideas on how I could avoid eating too much without causing offence to my hosts?