I believe that we were expanding more resources in Italy that the Germans were in defending it.
While a small theatre - very small by comparison with the EF - Italy was nevertheless a significant drain on Germany. Germany maintained an average of well over 20 divisions there throughout the campaign, some of which were amongst the stongest and best they had. Also, from late 1944, the Germans were maintaining more
divisions in Italy than the Allies were.
This question certainly begs further scrutiny. I've been wondering how best to measure up which side expended more resources in Italy. It's true that the Germans seem to have kept an overall slightly larger number of divisions in Italy than the Allies did, but then a straight count of divisions
doesn't tell the whole story either. For one thing, German divisions in Italy were notoriously understrength, particularly towards the end of the war - but then they probably weren't anymore understrength than German divisions elsewhere. Also, given the shorter line of communication, it was probably cheaper for the Germans to maintain a division in Italy than it was for the Allies.
I'm also unsure if/how RSI divisions and blackshirt brigades should be counted in the Axis total. The entry for 'summer 1944' on the page I linked to maintains that the Germans maintained 25 divisions in Italy at that time - but as far as I can see AOKs 10 and 14 at no time had more than 22 divisions between them in the summer of 1944, so the balance is presumably made up of blackshirts and maybe also the 16th SS. As far as I know the original four RSI divisions only became active by late 1944.
Maybe a straight hand-count of AOK 10 and 14 division-months held against 5th and 8th Army division-months from Sept. 1943 to April 1945 would give a better picture of who spent more manpower resources in Italy.
In terms of raw tonnage you're probably right that the Allies expened more in Italy than the Germans. However, it was tonnage the Allies could better afford. At a strategic level, the ROI was all in the Allies favour.
I'm certain that the Allies used far more shipping in the Med than the Germans did calculated from Sept. 1943, but on the other hand Allied tonnage spent there should be held against the much larger amount of tonnage the Allies would have needed if the Mediterranean was not open for shipping to and from the Far East.