Should i be worried about a sandy, dark brown (not black) sinking diarrhea with a lot of separate floating grease? i've also been extremely dizzy.

Two things...: (1) This diarrhea, if acute, could represent an infection that requires investigation and/or treatment and (2) the dizziness suggests that you may be dehydrated because of the volume loss in the diarrhea. As such, I would certainly be concerned and would see a doctor in an ED or urgent care center today for an evaluation.

Any weight loss?: If you have had unintended weight loss, you need to see a doctor for evaluation. Your dizziness may be due to dehydration, drink more water. For good health - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form. Practice safe sex, if you have sex.