I can only speak from our (relatively new) experience.
We are fortunate enough to live in a street with lots of young families and the kids are out playing all the time... there's about 5 or 6 of them out right now playing nerf wars. They climb trees and play football and take camping gear out to set up all summer and whenever it's not bucketing down in the winter. I honestly don't think he's feeling pressured at school either.
DH and I, although working full-time, arrange our hours to make sure one of us takes DS to school every day and we pick him up at least one, but usually two days/week.
He knows he is loved as we tell him and show him all the time. We play with him, as in proper play. Imaginex, Lego, games (headbands, giant jenga, game of life etc) so he most definitely isn't devoid of love or attention.
So, according to the undercurrent of blame running through this thread, the only 2 possible 'causes' are losing his papa last year and my struggles with my Mums suicide a couple of years ago. He exhibited anxious behaviour well before my Dad died though, it's just become more acute in recent months.
It breaks my heart to think I could be responsible in some way (even if not within my control) for his current anxious state 
Is it not possible that some children, just like some adults, develop a mental health problem which isn't necessarily caused by anything in particular?