I would guess your downvotes are from your huge generalisations of European and American cars. There are some high power-to-weight ratio engines in the US, and there are some low ones in Europe. So I could pick two examples that show the opposite.
Also, your assumptions on diesel and petrol are not useful - you cannot generalise the 'average' European car to be a diesel. There are many fleet cars which are diesels, sure, but there are also many which aren't.
Also, I think your sizing may not be indicative. I have only ever owned European and Japanese cars, and the smallest engine I have ever had was a 2.0 litre.
So your question comes across as stating some assumptions, then wondering why they are true - when in reality they aren't as cut and dried as that.
If we go with your generalisations, however, there is a very simple answer: pricing of oil and its products (petrol/gasoline)
In the US, there has not been the same driver to produce highly tuned/highly efficient engines as in other parts of the world, as gasoline has been available and very cheap. So engines can be big and simply machined - efficiency doesn't need to matter in this context.
Also, if we do include size, a larger capacity engine will burn more fuel per cycle, so in general, as size increases, consumption increases. As these engines will also weigh more, and the car carrying it is likely to be bigger you will also lose efficiency through moving a larger mass.