。
The eggs were sorted by size and weight.
Literal
Egg [topic-は] largeness [and-と] weight [by-によって] were-sorted.
大きさ and 重さ are noun forms built from the i-adjectives 大きい and 重い by replacing い with さ — a productive nominalization pattern that converts an adjective into an abstract quality noun. によって marks the means of sorting. 選別 is a suru-verb meaning 'selection / sorting.'