Learn Dutch: Wij wegen en verpakken het fruit. - We weigh and package the fruit.

Both the subject (wij) and the direct object (het fruit) are shared. The full, unreduced sentence would be: Wij wegen het fruit en wij verpakken het fruit. To avoid repetition, we drop the second wij and the first het fruit.

Why is het fruit dropped from the first half of the sentence, rather than the second half?

When you share an element that naturally comes after the verbs (like the direct object het fruit), Dutch omits it in the first clause and keeps it in the final clause. If you wrote Wij wegen het fruit en verpakken, it would sound awkwardly incomplete to a native speaker.

Why does the reduction rule work differently for the subject wij?

Because the subject wij comes before the verbs. When a shared element sits in front of the verb, Dutch does the opposite: you keep it in the very first clause and drop it from the second one.

Could I use conjunction reduction if het fruit had a different grammatical role in the second part?

No. A strict rule of samentrekking is that the omitted word must have the exact same grammatical function in both clauses. Here it works perfectly because het fruit is the direct object of both wegen and verpakken. If it were the subject of one verb and the object of the other, you would have to write it out both times.