The Gemara in Masechet Ketubot (103a) discusses why the Torah writes, “Honor your father and your mother” when it could have seemingly written “Honor your father and mother” (without including the Hebrew words "את" "ואת"). Our Sages expound the first "את" in this verse to include one’s obligation to honor his father’s wife (one’s step-mother) even though she is not one’s mother. The second "את" in the verse comes to include one’s obligation to honor one’s mother’s husband (one’s step-father) even though he is not one’s father and has merely married one’s mother after the passing of one’s father or after the parents divorced. The letter "ו" of the word "ואת" comes to include one’s obligation to honor one’s older brother.
The Rosh writes in one of his responses that there is no distinction between a paternal older brother and a maternal one. Maran Rabbeinu Ovadia Yosef zt”l rules that there is no distinction between one’s older brother or older sister, as one is obligated to honor them both. One must be exceedingly careful regarding this law, especially in our generation when familial order and authority is not as solid as it was in previous generations. Nonetheless, one must be sure to fulfill the commandments of the Torah and our Sages by honoring one’s older brothers and sisters properly.
The Rambam writes that the obligation for one to honor one’s older brother is not a Torah commandment; rather, it is only rabbinic, for the obligation to honor one’s step-parent is inferred by the Gemara from the word "את" and is considered to have been written explicitly by a verse in the Torah, however, the obligation to honor one’s older brother, which is only inferred by expounding the letter "ו", is not considered to stem from an open verse in the Torah and is merely a rabbinic obligation.
The Poskim disagree whether or not one is obligated to honor one’s older brother or sister after his parents have passed on. The Ramban writes that the reason for the obligation for one to honor one’s older siblings stems from the honor one must have towards one’s parents, for it is disrespectful to the parents if their children are not respected. After the parents’ passing, however, this reason no longer applies. Others are more stringent regarding this law.
Maran Rabbeinu Ovadia Yosef zt”l writes that although one is forbidden to call one’s father by his first name as we have established in a previous Halacha, nevertheless, it seems that there is no prohibition to call one’s older brother by his first name. One of the reasons for this is that the prohibition to call one’s father by his first name does not stem from the Mitzvah to honor one’s father; rather, it stems from the Mitzvah to revere one’s father. Regarding one’s older brother though, we only find an obligation to honor him but not to revere him. Similarly, all of the ways one respects one’s older brother need not be like one honors one’s parents. It is certainly forbidden to shame or rise up against one’s older brother or sister, for this constitutes a direct lack of respect and is a violation of this rabbinic commandment.