Is the earth getting heavier or lighter?

Sure, adults weigh more than (and are larger than) eggs and sperm. Where does that growth come from? Answer - food. Where does the food come from? Animals and plants. Where to animals get it? Plants. So it boils down to plants.

Where do plants get the matter that eventually gets turned into people? They get carbon from the air, water from the environment, some nitrogen and such from the soil.

So, whether it is people, or cows, or trees, or grass, or corn, all living matter grows by taking mass that is already on the planet Earth and recombining it into a new arrangement. More people, fatter people, etc are all still just rearranging the mass that the Earth already has. The only way that changes is when the aliens show up and start migrating here.

Short term memory loss!

The question was "Is the earth getting heavier or lighter? " (See OP)

I know it’s difficult, but try to see it this way.

There is no such thing as weight; there is only gravity.

If things had weight, everything would fall to the bottom of space!

A smart-ass answer to a question asked colloquially. Color me unimpressed. You old enough to drive yet?

You could try answering the interesting question: Is the Earth getting more or less massive?

Anyway, for the sake of the question, assuming there is a net mass gain, then, yes this would slow the rotation. But of course by an immeasurably tiny amount, as the gain is immeasurably tiny compared to the amount of mass already rotatiing.

And this assumes that angular momentum around the Earth’s axis of the incoming mass sums out to zero. There may well be something about the Solar System that means this isn’t true, so you’d have to account for this as well. Though again, ‘immeasurably tiny’ is the applicable description.