Is abstaining from eating hamburgers and their derivatives for a month—with the intention of losing weight—considered a valid vow?

Your vow is a vow of a permissible act, which is valid according to some scholars, and the preponderant opinion is that you have a choice between adhering to it or abandoning it. If you abandon it, it is preferable that you expiate for it with an oath expiation, which is: feeding ten poor persons, or clothing them, or emancipating a slave. If you cannot find any of these, then fasting three days. There is no blame upon you if you adhere to your vow and refrain from eating the aforementioned food throughout the month.