Question: Does Bhagavad Gita profess of forbid observing fasts
Answer: In Shrimad Bhagavad Gita Chapter 6 Verse 16, observing fasts has been forbidden.
Bhagavad Gita Chapter 6 Verse 16
Na, ati, ashnatH, tu, yogH, asti, na, ch, ekaantam, anashnatH,
Na, ch, ati, swapnsheelasya, jaagrtH, na, ev, ch, Arjun ||16||
It is stated that – O Arjun! This bhakti is neither successful of one who eats excessively, nor of one who does not eat at all, that is, neither this bhakti is successful of a person who keeps fasts, nor of someone who sleeps too much, nor of someone who remains awake a lot.
Therefore It is completely forbidden in this verse of Bhagavad Gita to keep fasts. Open your Gita and look in it.