Unable to get into a 'TT' position, is my bike fit wrong, or am I just fat?
A bike fit is not intended to make any position you can adopt on your bike work. 

If the bike fitter did their job correctly, then would have set you up for your current level of flexibility, strength and desired riding style. You say you are 'very comfortable', presumably in the position you ride in most of the time, so the bike fit should be good.

If you have only been cycling regularly since the summer, starting from less than ideal physical condition, I would not be at all surprised that getting into a slammed position on the bike is going to feel pretty horrible.

The good news is that you can lose weight and improve strength and flexibility over time, and you will be find it easier to adopt a more aggressive position.