Allaah has prescribed fasting and made it easy, hence Allaah says in the verses on fasting (interpretation of the meaning): 

“Allaah intends for you ease, and He does not want to make things difficult for you”

[al-Baqarah 2:185]

Allaah has permitted those who are sick not to fast in Ramadaan. 

The sick person for whom that is permissible is the person who has a real illness for whom there is the fear that it may be made worse or that his recovery may be delayed, or a sickness that is expected to occur because of fasting. We have explained that in the answer to question no. 12488. 

Based on this, if fasting causes the questioner to vomit or become dizzy because of physical weakness, there is nothing wrong with her not fasting in Ramadaan, but she has to make up the fasts, if she is able to. If she is not able to, then she must feed one poor person for each day. 

Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) was asked: 

What is the ruling on one who breaks the obligatory fast because of thirst? 

He replied: 

The ruling is that it is haraam for one who is observing an obligatory fast – whether in Ramadaan or making up a missed fast, or observing an expiatory fast, or fidyah – to break this fast. But if his thirst is so intense that he fears that he may be harmed or may die, then it is permissible for him to break the fast and there is no sin on him, even if that is in Ramadaan, if it is so bad that he fears he may be harmed or may die. Then it is permissible for him to break the fast. End quote. 

 And Allaah knows best. 

Majmoo’ Fataawa al-Shaykh Ibn ‘Uthaymeen, 19/question no. 149.