Why does the ground shake when titans walk? In the latest series, an experimenter told Eren that titans are very light despite their size. Why, then, does the ground shake when they walk?
It's probably not so much that the titans are very light eventhough they are really large, but that they are light for their size. Meaning that they're still really heavy, but not nearly as heavy as their size would make it seem.

Anime vs Real physics aside, if something really large was light enough not to make the ground shake, at least a little, they're probably not heavy enough to generate the needed friction to run, or if they were to move their body really quickly they'd leave their feet, or if they jumped they'd be in the air for much longer, or if they stomped the ground hard, they'd launch themselves into the air, etc.

All the interactions of the titans make them seem like they weigh enough to interact normally with their surroundings, just that for their size, they actually weigh a lot less than expected.