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I want to say:

He weighs 100 kilograms, which is too much.

But I am confused as to which relative pronoun to use, and why. The problem is that I don’t think the pronoun (der, die, das) is actually describing Kilo.

Er wiegt 100 Kilo, die zu viel sind.

That doesn’t sound right to me, as I don’t want to describe the word Kilo itself.

Er wiegt 100 Kilo, die zu viel ist

That also doesn’t sound right due to using ist with the plural.

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Er wiegt 100 Kilo, die zu viel sind.

In this sentence, the relative pronoun »die« refers to »100 Kilo«. In English this is:

He weighs 100 kilograms, which are too much.

But this is not what you wanted to say in Englisch. You said »which is«, so you used singular. So in the english sentence the pronoun »which« can’t refer to »100 kilograms«. It referes to something else.

Lets look at your second try:

Er wiegt 100 Kilo, die zu viel ist.

This is definitely wrong. Again »die« refers to »100 Kilo« which is in plural. So the verb must be plural too. »Ist« is wrong. »Sind« would fit, but this is already your first try.

The solution is:

Er wiegt 100 Kilo, was zu viel ist.

Here »was« referes to the entire previous sentence Er wiegt 100 Kilo (not to the concrete 100 Kilo). It is the same mechanism as in English.

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A relative clause that does not refer to a particular noun from the superordinate clause, but to the superordinate clause as a whole, is introduced with was:

Er wiegt 100 Kilo, was zu viel ist.
Sie hat auch Maschinenbau studiert, was für ihre Arbeit sehr hilfreich ist.
Er erreichte die volle Punktzahl, was seither niemandem mehr gelungen ist.

Rarely, adjectival welcher with an abstract noun is used instead to refer to the fact established by the superordinate clause; it does sound unusual and somewhat precious, though:

Sie hat auch Maschinenbau studiert, welches Wissen für ihre Arbeit sehr hilfreich ist.
Er erreichte die volle Punktzahl, welche Leistung seither niemand mehr vollbracht hat.

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