Our perception of what constitutes 'elderly' is changing. Older people are staying healthier for longer and pride themselves on retaining their youth, so the business of respecting our elders can be tricky. In times past, the elderly occupied an elevated position in society and were treated deferentially, but this can now seem disproportionate or even patronising. However, some people will expect this and you must trust your judgement.
In practical matters, always be patient. Older people are likely to eat more slowly, walk more slowly, and generally take life at a slower pace than their younger companions.
If you are an older person, show reciprocal patience and respect for your juniors. A polite response will go a long way. Reacting badly to what you consider to be an over-the-top demonstration of respect will embarrass and discourage younger people from acting kindly in the future.