Gemara

(Beraisa): "V'His'alamta" - sometimes you ignore an Aveidah. E.g. if a Kohen sees an Aveidah in a cemetery, or a Chacham sees an Aveidah that it is undignified for him to carry it... he ignores it.

The verse is not needed for a Kohen who sees an Aveidah in a cemetery. Returning an Aveidah is an Aseh. It is not Docheh the Lav and Aseh ("Kedoshim Yihyu") forbidding a Kohen to become Tamei. Also, Isurim are not overridden for (Mitzvos pertaining to) money!

Yevamos 5a - Question: What is Chachamim's source that an Aseh is Docheh a Lav?

Answer (Beraisa) Suggestion: Perhaps "A razor will not pass over Rosho" applies to a Nazir even if he is a Metzora!

Rejection: "Rosho" teaches that Tiglachas Metzora is Docheh the Lav for a Nazir to shave (his head).

Objection: The Isurim of a Nazir are weaker, since Yeshnam bi'Sh'eilah (they can be annulled). We cannot learn to a regular Lav!

Support (for objection): Why don't we learn from Nazir that an Aseh is Docheh a Lav and an Aseh? It must be because Isurei Nazir are Yeshnam bi'Sh'eilah. Likewise, we cannot learn from a Nazir that an Aseh is Docheh a Lav.

Kidushin 29a (Mishnah): Women are exempt from a Mitzvas Aseh sheha'Zman Grama (it applies only at certain times). They are obligated in a Mitzvas Aseh she'Lo ha'Zman Grama.

34a (Beraisa): The following Mitzvos are not Zman Grama: Ma'akah (building a railing around one's roof), Hashavas Aveidah, and Shilu'ach ha'Kan.

Berachos 19b: "Ein Chachmah... l'Neged Hash-m" -- wherever desecration of Hash-m's name is involved, we do not honor an important person.

Question (Beraisa): If an Avel (mourner) was returning from burying his Mes on a Tamei path, Kohanim may accompany him, due to his honor.

Answer (R. Aba): The path was a Beis ha'Pras. Its Tum'ah is only mid'Rabanan.

Question (Beraisa): Kavod ha'Beriyos overrides a Lav of the Torah.

Answer (Rav bar Sheva): It overrides only the Lav of Lo Sasur (do not turn from what the Chachamim say).

Question (Beraisa): A Kohen Gadol Nazir is Metamei for a Mes Mitzvah (even if he will miss offering Korban Pesach. This shows that Kavod ha'Beriyos overrides Torah laws!)

Answer: It overrides only something passive.

Rishonim

Tosfos (Yevamos 5a DH v'Achti): Some say that we do not learn from Tiglachas Metzora that an Aseh is Docheh a Lav and an Aseh that are not Shavah b'Chol (do not apply to everyone) because the Aseh of Tiglachas is stronger than a regular Aseh, due to Gadol ha'Shalom (it helps permit him to his wife). This is only like the opinion that a Metzora Muchlat is forbidden to his wife.

Teshuvas Avnei Milu'im (22 DH Kosav): Tosfos holds that only the opinion that permits a Muchlat to have relations learns from Tiglachas Kohen Metzora that Aseh Docheh Lo Sa'aseh v'Aseh if the latter is not Shavah b'Chol. It seems to me that all hold that we cannot learn, for all forbid a Metzora during the seven days he counts between the two shavings.

Magihah: I do not understand. If normally an Aseh is not Docheh a Lav and Aseh that are not Shavah b'Chol, the Muchlat can never shave the first time, and he will always be permitted to his wife. Why is Gadol ha'Shalom a reason to permit?

Question (Rif Bava Metzia 16b): The Gemara says that the Aseh of Hashavas Aveidah does not override the Aseh and Lav of Tum'as Kohanim. There is also a Lav not to ignore an Aveidah. Why did the Gemara omit this?

Answer (Rif): Only Mitzvos Aseh are Docheh, therefore the Lav of Hashavas Aveidah is irrelevant here. When the Gemara discusses whether or not Kibud Av va'Em is Docheh Hashavas Aveidah, it mentions the Lav and Aseh of Hashavas Aveidah, for both are relevant.

Question (Ritva Bava Metzia 30a DH l'Mai): An Aseh is not Docheh even an Aseh by itself. Why does it say 'an Aseh is not Docheh a Lav and an Aseh'?

Answer (Ritva): Since the Aseh of Hashavas Aveidah is Shavah b'Chol but the Aseh of Tum'ah is not, the former would be Docheh the latter if not for the Lav. Even the opinion that an Aseh of (Tiglachas) Metzora is Docheh a Lav and an Aseh that are not Shavah b'Chol, this is only because the Aseh of Metzora is stronger, for it permits a man to his wife.

Question (Ritva, ibid.): The Lav and an Aseh of Hashavas Aveidah are Shavah b'Chol. They should be Docheh the Lav and Aseh of Tum'ah, which are not Shavah b'Chol!

Answer (Ritva): The Lav of Hashavas Aveidah is transgressed passively. If he would return the object, he would actively transgress Tum'ah.

Question (Tosfos Kidushin 34a DH Ma'akah): The Gemara says that women are obligated in Aseh she'Lo ha'Zman Grama such as Ma'akah, Hashavas Aveidah and Shilu'ach ha'Kan. Each of these has a Lav, so it does not matter whether or not the Aseh applies to women. In any case they must do the Aseh to avoid transgressing the Lav!

Answer (brought in Tosfos): If they were obligated only in the Lav, a different Aseh could be Docheh the Lav (e.g. if she needs to offer a bird for Korban Yoledes and the only bird she can find is sitting on eggs).

Question (R. Yosef of Eretz Yisrael): The Gemara (Shabbos 25a) says that the Aseh to burn Pasul Kodshim is not Docheh the Lav and Aseh of Melachah on Yom Tov. Why doesn't it say that for women, who are commanded only about the Lav, the Aseh is Docheh the Lav?

Answer (R. Yosef in Tosfos, ibid.): Since there is an Aseh with the Lav, even though women are exempt from the Aseh, this shows that the Lav is more stringent, so an Aseh is not Docheh it. (This refutes the previous answer.)

Rashi (Berachos 20a DH Shev): Not offering Pesach is passive. The Torah never forbade a Kohen Gadol or Nazir to become Tamei to a Mes Mitzvah, therefore, it did not ask from this.

Rebuttal (Tosfos 20a DH Shev): If so, we should never say that an Aseh overrides a Lav, rather, the Lav was not said there! Rather, we cannot learn from Nazir, since Yeshno bi'Sh'eilah, and Isurei Kehunah are not Shavah b'Chol.

Poskim

Shulchan Aruch (YD 372:1): A Kohen may not enter a Beis ha'Pras. He is permitted in order to marry or learn Torah, if there is no other path, or to follow a mourner to console him.

Gra (1): Tosfos and Rav Hai Gaon say that we do not learn from Tum'ah because it is not Shavah b'Chol. The Ramban says that some texts of the Gemara explicitly say so. However, if so we retract from what we said above (that we permit only Tum'ah mid'Rabanan to accompany an Avel). Therefore, the primary answer is like Rashi said. Similarly, we do not learn from Yibum that an Aseh overrides Kares, for the Lav does not apply there.

Acharonim

Avnei Milu'im (ibid., DH v'Nir'eh): Tosfos (Nazir 41b DH v'Iy) says that here, Nazir is considered Einah Shavah b'Chol, but the Sugya on 58a considers it Shavah b'Chol. They argue about the nature of Nezirus. Mahari Basan says that it is like a Neder; he forbids on his (appropriate) limbs wine, shaving and touching Tum'ah or entering Ohel ha'Mes. This is Shavah b'Chol, because anyone can take such a Neder. The Maharit holds that Kabalas Nezirus is Mekadesh the person, similar to a Kohen. The Torah put the Isurim on Nezirim, therefore they are not Shavah b'Chol. This is how the Rambam rules.