All buildings can carry their own weight (or they would fall down anyway by themselves). They can usually carry a bit of snow and a few other floor loads and suspended loads as well, vertically; so even badly built buildings and structures can resist some up-and-down loads. But buildings and structures are not necessarily resistant to side-to-side loads, unless this has been taken into account during the structural engineering design and construction phase with some earthquake proof measures taken into consideration. This weakness would only be found out when the Earthquake strikes, and this is a bad time to find out. It is this side-to-side load which causes the worst damage, often collapsing poor buildings on the first shake. The side-to-side load can be worse if the shocks come in waves, and some bigger buildings can vibrate like a huge tuning fork, each new sway bigger than the last, until failure. This series of waves is more likely to happen where the building is built on deep soft ground, like Mexico City. A taller or shorter building nearby may not oscillate much at the same frequency.