Is a 'congratulations' gift in order for a person who is getting a new job and will be making more money than me right away?
This somewhat depends on your friend's motivation for taking the new job. Is it really for money or is because they really want to leverage their career in the right direction?
If the answer is yes to the latter, then it's a nice gesture to acknowledge your friend's accomplishment. If they are truly your friend and they've worked hard to get this position, then they should know that you are delighted as well. If they've taken the job only to increase the width of their wallet - don't worry about it too much.
I'd love to take my Mother out for a nice dinner in celebration of her weight loss. Obviously, that might not be the best idea. Do you have other suggestions?
Your Mother would probably love the opportunity to buy a new outfit in a new size at her favorite store. If she's lost a significant amount of weight- her life will be changing for the better. She may have new hobbies and interests that she wasn't able to participate in before. She might like the chance to go somewhere warm where she can dress differently and feel great about herself. If this is the case, a hotel stay or an airline ticket to a beautiful beach is a great surprise.