What causes mountains to get taller?

Answer 1

They grow taller because the tectonic plates shift upwards and cause them to move slowly taller

They rise taller because the earths tectonic plates are ever shifting, with one shifting underneath its adjacent mate, producing a massive uplift of the mate. This typically results in tidal waves (in recorded history), climate change, and of course, landmass upheaval, producing many of the mountainous ranges we know today.

Considering the very slow process of mountain upheaval, it is doubtful that it would cause any tidal waves.

It is correct however that as tectonic plates collide, mountains can be forced upwards as one plate subducts under another. More typically however is that the mountains rise as the plates collide and the crust buckles upwards. Of course volcanic mountains can grow in size from the deposition of volcanic materials during eruptions.

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Perhaps a geologist or seismologist could join in and give us all a primer on how tectonic plate movement, and the force of friction on geological scales, can unleash massive energy transference, such as to a body of water. Or perhaps not.

Please in the future, read my entire answer, and try to understand the entire context. Or perhaps not.

Answer 2

Depends on the Mountain.

Some mountains, like fold mountains which are caused by two continental plates converging, grow taller as the plates continue to converge. Like the Himalayas are right now.

Volcanic mountains would grow due to continuous volcanic activity releasing magma that would pile up making the mountain bigger, like Mauna Leia in Hawaii.

Fault-block mountains are caused when one side of a fault drops below the other side. If the fault continues to fall, the mountain will get "taller", at least relative to everything around it.