No one thinks is weird that an old man like Mr.Fredriksen

Adrenaline?

This is a fun question.

If I had to go with the simplest answer, the chair was a gag and used in trailers.

If I wanted to go artistic, I would answer that he and the house were having a symbiotic relationship. The chair isn't lifting him, its the house lifting the chair.

If I wanted to answer realistically, as we age we surrender to our failing health to a point of choosing convenience (the chair) over realizing what potential we still have left (climbing blimps).

I always believe film sends messages and contradictions are picked up conscientiously or not.

But isn't that part of the whole point of the film? He'd let himself give up. The adventure helped him to gradually realise his potential and... Be adventurous!
Plus, as you say, it's a fantasy.

This is honestly what made me dislike the movie the first time I saw it. I could buy into the fantastical elements (talking dogs, Kevin, balloons lifting the house, etc) but I did't understand how an elderly man with a cane could suddenly run and climb up the side of a blimp. It really took me out of the film.

However, on later viewings, I think I understand more that Carl wasn't as weak and frail as he seems to be. He has let himself give up because he lost the love of his life. You see him easily climbing up that hill with Ellie when they are both aged, but the next scene that requires any physical movement out of him has him moving slowly and painfully. This is more because of the emotional pain, not physical. When he is distracted by something or someone else (Russell) or is driven to do something (i.e. tug of war with the construction worker over the mailbox, or climbing the blimp) he pushes past the sadness and becomes more lively and agile.