Usage of "would have been"
Solution 1:
In this case either "would have been proud" or "would be proud" are acceptable. The meaning would be the same. The very slight difference between the two is a matter of the speaker's attitude or viewpoint toward the time frame of Jimmie's existence.
We are proud of you, son. Jimmie would have been proud of you, too.
The attitude of the speaker focuses on Jimmie's existence in the past with no extension into the present.
We are proud of you, son. Jimmie would be proud of you, too.
The attitude of the speaker allows for Jimmie's existence without reference to the past time frame.
Solution 2:
To some extent they're interchangeable, but I think there's a slight difference in implication. If I say:
Jimme would be proud of you (if he knew/could see this).
it can imply that Jimmy potentially had the opportunity to see the event but didn't due to some 'temporary' event (not finding out yet, not being there at that particular moment). Whereas:
Jimmie would have been proud of you (had he still been alive/living here).
has slightly more of an implication that it was not possible for Jimmie to witness the event due to some fairly 'definiitive' previous event, e.g. dying, moving away etc.
However, these are implications rather than hard-and-fast differences in meaning. To some extent, they are interchangeable with either meaning.