Let us not go round the houses. Take this straight to the face.
When I pity somebody, I lower them in my own consciousness to the rank of the pitiable. Which is to say, I attribute weakness to them. Which is to say, I diminish them in comparison with myself.
And the hastily offered help that follows — which is frequently not concrete assistance but emotional support — only closes the psychological transaction in your mind. He is below, I am above.
Now a disclaimer, before I get an explosion in the face: obviously this does not apply to every expression of sympathy, and even more obviously I am talking about other people, not about you.
And still, a tip. Dropping your pity onto another person severely narrows their available responses and traps them in a corner. Either they resist, and come out looking ungracious, or they accept your pity gratefully, and come out looking weak.
So here is the tip I promised. Ask. Ask directly, and give an authentic opening for retreat.
Sounds obscure? Let me demonstrate.
Look, this might be entirely in my head, and I may be barging through a door that is not mine, but you have seemed thoroughly low lately. Is there a chance you need help? If so, feel free — and if you are fine, feel equally free to tell me you are not interested.
Notice what that construction does. It states the observation, admits it might be wrong, offers help, and pre-authorises refusal without cost.
Which means the person can decline without having to reject you, and can accept without having to be a case. That is the whole difference between support and condescension, and it lives entirely in how the offer is phrased.