It's mainly fasting for enemy religion reasons that we are against here in the JoS. And fasting to the point of weakness and dizziness is bad because it will open you to enemy programmings and thoughtforms, and weakness in general is to be avoided in Spiritual Satanism. A strong body helps a strong mind and soul.
But fasting for short periods of time, for certain people, for certain reasons, is fine. I've known people who felt so much better after a fast of a few days, making sure to get vitamins but no food. The OP wrote doing this after eating too much greasy food, so a short fast can help clean the system.
If you decide to do a fast for health reasons, go with how you feel. If you feel starving and like you need a steak dinner feast, quit the fast. If you're feeling great, then continue until you don't feel great anymore. If you feel alert and revitalized during your fast, great. Once you start feeling weak, fuel your body.
Always do what makes you feel strong and healthy.