There's a problem with this question. The average weight of one child is 85.6 pounds.
When weighed in pairs we would expect a combined weight to be around 160-170 pounds.
The average pair weighing is 85.4 pounds. That means an average of 42-43 pounds per child.
Despite this discrepancy, I offer the following solution.
The first observation is the gap 80-82; there is no pair weighing of 81lb.
The next observation is that if we add all the group weighings we get 854, because:
80+82+83+84+85+86+87+88+89+90=854,
but the combined weight of the kids is 856.
The next observation is that 856/4=214. We'll see later why this is significant.
The discrepancy 854 versus 856 shows that the weighings were not symmetrical, that is, that not all the kids had equal involvement in the weighings.
The 10 pair weighings are not distinctly unique; they represent values occurring several times over.
First we look at the lowest pair weighing of 80lb. Two kids, each weighing 40lb would produce this value. These are the lightest kids. Similarly two kids, each weighing 45lb would produce the value 90lb.
The value 81lb is missing from the list, so we have to exclude a 41lb kid because, when weighed with a 40lb kid their combined weight would be 81lb.
Therefore I suggest that amongst all the kids their weights are 40, 42, 43, 44, 45 pounds.
Also, the arrangement of pairs is:
40+42, 40+43, 40+44, 40+45
42+43, 42+44, 42+45
43+44, 43+45
44+45, producing the following weighings:
82, 83, 84, 85
85, 86, 87
87, 88
89.
When the lightest kids are weighed together we get 40+40=80 and when the heaviest are weighed we get 45+45=90. So we have covered the complete set of values in the weighings.
When we add the set of unique weights 40+42+43+44+45=214=856/4.
Therefore, if we have 4 kids of each of the weights 40, 42, 43, 44, 45 we get 160+168+172+176+180=856lb, which is the total weight of all the kids. But there are not 10 but 20 of them.
This is the most fitting solution I can offer to this question. The average weight of the kids is 42.8lb which is consistent with the weight of a young child, or "kid".