I've helped healthy people by holding doors because of what (or who) they were carrying or if they had to use a walker and the doors weren't automatic. Maybe that looks funny now, because I usually use a cane. Well, I wear a smaller purse that slings across my body, so I have a free hand. People have always seemed relieved. If I'm not sure if someone needs help with something, I just ask, "Would you like some help with that?" Usually, they'll either say, "Yes! Thank you!" or "No, I've got it, thanks." I've never noticed anyone being offended by my asking. Sometimes I'm not doing very well and I need help, too. Other times I am doing fine. I give the same types of answers.
Maybe if you're older, grew up in the mid-west and/or not in a big city, it's more likely that you were brought up to think it was common courtesy to help with some types of things. I was. A person didn't need to be disabled to need a bit of help. It didn't make you less of a person to accept a bit of help.