Help diagnosing problem with old bike - probably silly newbie question...

[Looeez]

I got an old bike recently that I'd like to use when I want something lighter than my cruiser.

Although it's some other brand I haven't heard of, it looks a bit like a Schwinn Breezer or Collegiate or similar from the 70's or so.

Anyway, while riding it to test it out I noticed that when I went off a particulary high curb the bike didn't seem to "bounce" and the derailleur part (I think) seemed to catch on the curb.

I'm not sure what might cause this. I'm going to check the air in the tyres but other than that I'm not sure what might cause this. Or am I just so used to my big, fat tyred cruiser and this is what happens on bikes with skinny wheels?