Hello. You kind step mum. 
I have a bit of experience; might be similar to yours although through MN you can hardly know if my experiences are relevant.
One of my step sons is underweight. It is moderate. He is probably on the spectrum and he chooses to control his diet as one of his oddities. I don't know much about how to talk about unusual personalities, and I don't want to be rude. Let's face it - We all have a personality - and DSS is more unusual.
His thinking patterns are independent and he is pedantic, and with food, I find, he isn't easily swayed off his own track. He wants to be healthy. But his view of healthy lies within controlling himself and not being 'free' to eat spontaneously.
This was less visable in him at 14 but has become more so now he is adult. I could see this aspect at 11 years old when he began to get very thin. Already, at that time, he preferred lemon sorbet to creamy ice cream. Incidentally, he got very angry and emotional after about 14, he struggled to cope, and that has eased off completely. He argues his view calmly these days, but unswervingly, at length
. And he eats a narrow diet.
I have found ways to make small adjustments to his diet.
He likes nuts and seeds and fruit so they are in bowls on the worktop. I used to stir cheese into savoury cooking and provide chocolate and popcorn which he found hard to resist. He wouldn't eat those now. He scrutinises ingredients.
I have found that I should worry less and just feel I have done my best.
My DSS goes to the loo every meal time (no, I don't think to be sick). I think it is an anxiousness within him. A feeling to output because he is inputting. And to pace himself with eating.
I let my DSS get on with it. I mention sometimes he's a little under weight. Mostly I comment when he looks well.
Regarding the Fitbit - is there more of the Apple Watch type thing that isn't just for fitness. Perhaps he'd be attracted to the tech. A phone can track your steps, but a Fitbit will feed his issues with vibrations perhaps. The tech watches are expensive but you might believe it would be better to not let him be motivated by a Fitbit. They are designed to make you walk more.
Could you motivate your DSS to eat more chicken? All the body builders do that.
I would take the fact that at 14 he needs calories, so if I was you, I would be less fussy about the nutritional content and serve doughnuts!