Yes, it's correct—in India
When I first read your sentence, I thought that it misused the word reservations. But I was wrong. I am an American native speaker, and I just did some googling and learned that the sense of "reservations" in your sentence is standard in India but not in Britain or America. It is not mentioned in the Merriam-Webster article that you linked to, though there are some closely related senses.
Outside of India, the closest word for this sense of "reservations" is quotas. But even the word "quota" is ambiguous. The relevant sense is the third listed by Merriam-Webster. But there are common senses of "quota" not listed by Merriam-Webster, that have the opposite meaning, such as a goal for a quantity of something to be produced (as in "meet your quota") or even a maximum quantity of something that you are permitted to consume (as in "exceed your quota"). See Wiktionary. You could not use the word "quotas" for India's constitutional reservations without explaining it and expect to be understood.
You might need to explain it
As always, Know Your Audience. If the audience for your writing is people from India, then your use of reservations is correct, standard, and needs no explanation. If you are writing for people in Britain or America, then you should still use the word "reservations"—no other word will do—but you must explain it, just as you would explain any specialized or esoteric terminology when writing for a general audience. This article by the British Broadcasting Corporation illustrates how to do it:
India's constitution, adopted in 1950, inaugurated the world's oldest and farthest-reaching affirmative action programme, guaranteeing scheduled castes and tribes—the most disadvantaged groups in Hinduism's hierarchy—not only equality of opportunity but guaranteed outcomes, with reserved places in educational institutions, government jobs and even seats in parliament and the state assemblies.
These "reservations" or quotas were granted to groups on the basis of their (presumably immutable) caste identities. The logic of reservations in India was simple: they were justified as a means of making up for millennia of discrimination based on birth.
After this definition, the article freely uses the word reservations in the sense that you have in mind. The reader can now be expected to understand when "reservations" denotes this new concept.
In this context, the quotation marks around reservations help indicate that the author does not expect the reader to already know this sense of the word, and is now defining it. Putting the word in italics is another way to indicate that you are defining a new word or a new sense of a familiar word. Notice also that the article provides some background information before defining the term and states the rationale for the reservations. This makes the definition easier to understand. The background paragraph even uses the word reserved, which helps the reader see why the word "reservations" was chosen.
More sources of confusion
By the way, this word will be especially prone to confusion in America, where an Indian reservation means a land area reserved to native Americans, where they enjoy rights similar to those of an independent nation. So, you should not use the phrase "Indian reservation" to refer to the distinctively Indian sense of "reservation".
Lastly, weaker sections is suggestive but not clear. The phrase disadvantaged groups makes clear what kind of people reservations in India are intended to benefit, without going into detail about the castes and social classes.
