Why are italics lighter than their upright counterparts?

Italics were used to save space (and paper) by Francesco da Bologna .

That’s unfounded speculation. See Cramsie, The Story of Graphic Design, p. 89. 

It has been thought that Aldus adopted this cursive humanist script as a space-saving device, but not only is there no quote or comment that supports this supposition, when the text is set in the same size as his roman type it does not increase in length. What is more certain is that his books benefitted from the popularity of the humanist script, which was held as a model for handwriting among educated and literate Italians.

And Updike proposed that Aldus used the italic because his Greek types, which matched contemporary writing hands, had been successful:

The adoption of an imitation of a cursive hand by Aldus for his new fonts is not wholly explicable by the wish for a compact type. His italic types were only a development of an idea already put into effect in his Greek fonts. The older Greek manuscripts employed formal, simple characters, separate from each other and with comparatively few ligatures or contractions, which adapted them very well to translation into type; but Aldus preferred to imitate the cursive Greek handwriting of his time, which was filled with an immense number of ligatures, contractions, and unnecessary complications. Despite their faults, these cursive Greek fonts hit the popular taste. So when a small, compact type was wanted for editions of Latin classics, etc., I suppose it may have seemed to Aldus natural and clever, to do for Latin letter-forms what he had done for old Greek letter-forms. It may be, too, that Aldus adopted a cursive letter for his new font because it suggested the popular and informal character of his projected series. Whatever his reasons, the result was the Aldine italic.

The following is completely anecdotal coffeetable psychology that I'm making up as I go along: 

Upright roman letterforms are static, akin to bodybuilders and weightlifters. Italic letterforms are more dynamic, they echo a quicker writing style, so they’re akin to runners and jumpers.

We’re psychologically hardwired to perceive objects that imply movement as lighter as those that imply sturdiness and reliance — and we expect them to be that way. 

But even if we limit ourselves to writing alone: writing upright letterforms is slower, and when we write slower, we tend to push the writing tool harder into the surface (so it’s easier to maintain a consistent stroke while going at a slow pace). Writing italic forms is faster, and when we write faster, we tend to push the tool less, we let it glide.

So as a natural outcome, the italic letterforms tend to be lighter than the upright ones, even coming from the same hand. That “natural” consequence results in our expectations for what’s “normal” to be formed accordingly. 

Seeing bolder italic forms being used alongside lighter upright forms is just as confusing as seeing a heavyweight boxer moving swiftly and gracefully next to a ballet dancer who stomps around clunkily. 

By similar mechanism, we perceive “printed” letterforms to convey more objective information while “handwritten” letterforms to convey subjective opinion. So by convention, in newspapers news are printed in upright while quotations or opinions are printed in italic. If we reverse the convention, many readers would be confused. 

Indeed, and you are right that some of the obliqued-roman italics are insufficiently distinguished, i.e. slant in itself is not adequate. Of the three conventional properties of italics—slant, distinctive (cursive) construction, and horizonal compression—I think a useful italic always needs at least two.

A question for the type designer or typography to consider is how will the italics be used. There are several conventional uses for italics in text—for semantic emphasis, for citations, for transcription—and while a good italic should be able to function in any of these roles, some might be better suited to one or other. The vary narrow italics of the Garamond tradition work very well for emphasis and adequately for citations, but not so well for transcription, where one wants the roman and italic to be easily distinguished but have a similar presence on the page. That’s why Brill italic, which is used a lot for tanscription, is so wide: