Worried about son's eating

[Rosebel]

For months now, since March my son has eaten a very limited diet at home. Yogurt, chicken satays and very rarely banana.
GP said weight is a bit low but nothing worrying.
He goes to nursery 4 days a week and always ate well there so I thought at least he's eating other things most of the week.
Except for the last two weeks he's become picky at nursery too. He'll eat cereal there but then often doesn't eat the rest of the day.
I spoke to the GP again but they said as long as he's got energy and isn't too tired and is drinking plenty not to worry but they could refer us to a dietician if we wanted.
I'm not sure that would help. I've tried everything, ignoring, encouraging, eating with him, offering him choice, offering him food off my plate but nothing works.
He's 2 with very little speech so can't tell me why he doesn't want to eat.
Initially I thought it was just a fussy phase but it's been months at home and now nursery too.
I am worried. He gets ill a lot and I'm sure not eating is part of the reason.
Has anyone had a child who got over this after months? Did you do anything or did they just get over it? AIBU to be so worried about his diet?

I have one like this. They have sensory eating issues. I would despair about the lack of balance in the diet. They never got any better but are now grown, very tall, none the worse for it. Sometimes I wasn't all that happy their diet but at least they were eating.

When DS did this I just fed him whatever he asked for. Chocolate for breakfast was even OK. If he'll eat cereal I'd get some healthy ones and feed him those for breakfast and lunch. I reasoned some calories (in whatever form) were better than none! He's now 7 and the least fussy kid on the planet so something clearly worked.

I hope he out grows it. He doesn't even eat cereal at home and strangely hates chocolate unless it's KitKat and then he might eat a bit.
I just know his diet is so unhealthy and he even refused yogurt this morning! I worry about him getting sick of eating the same thing and then refusing to eat at all.