"DC to AC conversion is costly conversion of energy right?"
Yes.
" Does efficiency from DC to AC change if you have large or small inverter?"
Not necessarily. If the same amount is pulled through two diffrent sizes, the total loss will be similar as long as their both the same design.
Internal inverter loss is due to its component's and design. You could put two of the same size and type, next to each other and see a difference in loss. Odds are unless one was inferior to the other, the difference is neglectable. Another factor is the bigger ones may have more features. If the features are always on (Bluetooth, lights, display...),their will be more loss than a smaller one.
Most of the loss is because you have to change DC to AC then step it up through a transformer or a multiplier. There's several ways to do this. The "Pure Sine Wave" systems are better, but can have more loss then the lesser ones.