Weight is not a factor for home energy storage, there is no need for lithium cells.
That depends on your living situation. I live in a third-floor apartment, so weight is very definitely a factor.
The apartment building can have unified power backup in its foundation/basement.
If you reduce the energy density by a factor of 10, the weight for power backup needs will still be far lighter than the concrete.
Weight always is a factor since heavy batteries cost more to transport, period. It's always relevant, not least for the installation too.