AC converter, step up or step down, which is more efficient, which loses more energy? why can't support large power and being small
I will try to answer your questions the simplest way possible:

A step up converter is almost always an iron-core based transformer. 
 

Simply because it's the simplest and most cost effective. A transformer easily converts 110V into 220V, or the reverse, at 60hz without any circuitry. The only problem is that transformers are big and bulky. A 500W transformer will weigh in excess of 5 pounds. A 2kW+ over 30lb. This is indeed because of heat dissipation and thermal constraints due to efficiency. The more powerful, the more power lost, so the bigger the transformer needs to be. 



A step down converter is actually a very simple product. It has very little weight because there is no transformer.



Source: https://www.homemade-circuits.com/how-to-make-220v-to-110v-dc-converter/

This simple circuit can easily handle 2000W because it simply needs to lower the voltage. There is basically no loss at 15A maximum.  



The issue with dual step up/down converters right now is that there is no cost effective way of converting 110VAC to 220VAC without using a transformer. There exists such products, but they are highly complicated and cost a fortune and isn't much smaller than a transformer of the same power capabilities. Someone correct me if they find one that is less than a few thousand dollars...

I did see actual papers on making a product like you want: 

https://www.researchgate.net/publication/277673392_Single-phase_direct_AC-AC_boost_converter

Not sure if it is consumer available yet.