Paisly - I was pondering this very q's the other day!
I think the problem is the context in which the term 'proud' has been used in the past. Generally we connect it with someone of higher position (adult, mentor, boss, leader, teacher etc) saying it to someone of less experience. And recognising someone's learning experience and respecting the way they have healthily integrated it, is not elevating ourselves. It is just generally that those who say "I'm proud of you" have already reached the 'elevated' position on similar experience themselves. But that doesn't necessarily mean the person saying "I'm proud of you" got there through any accomplishment - sometimes it can merely be an age thing.
However, I guess what you are talking about is the odd feeling when saying it to your peer. I would hazard a guess that you would probably only say it to someone you feel close to. And if that person is genuinely your friend or peer, then they will recognise that you have had the detachment to observe objectively what they have been doing and it's really an acknowledgment of how much you are happy for them, for their reward, for their determination, for their gift - and basically for them!
Maybe we should all start using it more so it loses it's elevated connotation.
It's like saying "I love myself". I remember when my daughter was around two, at that age when they say "I love Mum, I love Dad, I love Grandma etc etc through the family members". She would always finish off with "And I love myself!" with this huge smile on her face. I used to love the fact that she was so naturally emotionally intelligent. But at some unfortunate point in this culture, we have to stop thinking we love ourselves that overtly.
Anyway, I have learnt, like anything, it is not the words necessarily but the way the person says it and the intonation and intent. So use the term proudly if you really mean it