The best support you can give to anyone you love is your wellness. When you are well, joyful, fun, and happy, you are the greatest gift to everyone around you. That's when you inspire wellness, joy, and fun within them. When you take care of yourself, you are in a much better position to take care of others.
Your tiredness, sickness, and inability to look after yourself does not support or help anyone. Your loved ones don't want to be the cause of your unhappiness or exhaustion. They want to be the cause of your joy and wellness.