Sefer Ha'Chinuch
Esav’s malach wanted to get rid of Yaakov and all his descendants, but was unable to do so, although he did injure him. This can be understood as an eternal message through the ages: Esav’s descendants cause us a lot of distress during the period of the Exile, but we must always remember that they will never destroy us entirely, and just as the sun shone on Yaakov and healed him, so too the sun of Moshiach will shine and heal us from our distress and redeem us speedily in our days.
Seforno
The prohibition of eating the sinew of the thigh is to show that, no matter how unfavorable the odds may appear to be, Jews must fight for survival, notwithstanding any physical limitations.
Chizkuni
This negative mitzvah is in essence a penalty for the bnei Yisroel for all generations because they left their elderly father alone, as is mentioned in verse 25, "Va'yivo'seir Yaacov l'vado." The brothers were physically powerful and should have stayed with him just in case he had some need, rather than going ahead. This negative mitzvah will serve as a permanent remembrance and will serve as a reminder to escort and accompany those who need it. From this incident Yaakov learned to escort Yosef when he sent him to find his brothers.
Rashbam
This mitzvah is not a punishment. Rather it is a memorial to remember Yaakov's phenomenal strength to overpower an angel, and also to remember HaShem's kindness in saving him from death at the hands of the angel.
Alshich
The prohibition of eating the sinew of the thigh is intended to serve as reminder to Jews to distance themselves from any evil, even a particular evil that has not yet become officially forbidden (such as marrying two sisters). Jews are forbidden to eat the thigh muscle, as a reminder that even the saintly Yaacov was held accountable for his sin.
Rivo
This mitzvah is a remembrance of the miracle that Yaakov was saved from the attempt of the angel to totally do him in. To serve as a remembrance that Yaakov was injured and endured pain in that sinew. This is akin to someone who often suffered from headaches. Even when he is free of pain he would refrain from eating the meat of the head of an animal as a remembrance that he often suffered aches to his head.
Radak
This mitzvah serves as a remembrance that Yaakov through his great cleavage to HaShem merited to have this prophetic encounter (see Rambam Moreh N'vuchim 2:42) Belief in prophecy is one of the cornerstones of our belief, so it deserves a memorial.
Rambam
Those who assert that the mitzvah of the sinew of the thigh, or any other mitzvah, references historical events, are mistaken. The reason Jews abstain from eating the thigh muscle, is not because Jews descended from Yaacov whose thigh muscle was injured in the confrontation, but because of G-d's commandment at Sinai, to do so.
Lubavitcher Rebbe
The theme of the mitzvah of Gid HaNesheh is to acknowledge G-d’s protection and providence over His people Israel so that they will not perish in their exile among the gentile nations. This mitzvah includes two extremes elements of the event (the commemoration of an event of very general significance; and the concentration on one particular dimension of the event) which evokes an (intellectual) rationale.
The entire creation “came into being solely from the truth of His being” and is controlled by His providence. With regard to the creation as a whole, He manifests His providence on every individual according to its positive virtue, (i.e., the extent to which it serves the Torah and the Jewish people). This is reflected in the general aspect of this mitzvah.
Nevertheless, G-d’s primary desire and choice focuses on the Jewish people alone. The commemoration of Yaacov’s deliverance involves only one dimension of the event (and emphasis is placed on only one particular element). This reflects the nature of the Divine providence which was focused on Yaacov (and on the Jewish people, his descendants).
This concept is emphasized through the mitzvah of the Gid HaNesheh in which the general commemoration of Yaacov’s deliverance is associated with one particular dimension of the event. This teaches us that every particular dimension was related to his deliverance as a whole event.
