Shabbat Chazon is named after the haftara, which together with that week’s other readings, is the meeting point of three biblical uses of the word eicha (how). Moshe (in the parasha) says: "How can I bear alone your trouble, burden, and quarreling?" (Devarim 1:12). Yeshaya (in the haftara) says: "How did the trustworthy city turn into a harlot, the place full of judgment... now is full of murderers?" (Yeshaya 1:21). In the Book of Eicha, Yirmiya laments: "How did the populous city sit alone, become like a widow?" (Eicha 1:1).
The midrash (Eicha 1) uses a parable to contrast the three mentions of eicha. There was a noble woman who was observed by three close friends: one saw her in successful times; one saw her in her "haste;" one saw her in her disgrace. So too, Moshe asked eicha during the time of Bnei Yisrael’s honor. Yeshaya asked it in their struggles. Yirmiya used it in their disgrace.
We can understand the parable with a further parable of a sick woman who was seen by three doctors at different stages of illness. Likewise, Moshe was able to discern in a basically healthy nation symptoms that foretold future problems (Rashi highlights some of the troublesome attributes of stubbornness that the people were settling into). Moshe understood that exile would apparently be needed. Yeshaya observed the nation when it was already sick, comparing the one-time righteous nation to a harlot. However, the nation would retain its independence and Temple for close to 200 years. Yirmiya saw the nation in absolute ruins, when the people had already been sent into exile and the Land was barren and destroyed.
The last pasuk of Eicha seems to paint a picture of utter hopelessness. "For if You have been disgusted by us, you have been furious at us to an extreme." We have the minhag to complete the reading not from this last pasuk but from the preceding one: "Return us, Hashem, to You and we shall return; renew our days as of old," thus avoiding the bitter ending from remaining in our mouths. The midrash explains that even the last pasuk leaves hope. The first part of the pasuk is a question: did Hashem become disgusted with us? The answer is: no, he is just very angry, but the love is still there, and the anger will subside. Therefore, there is still room for "renewing the days as of old."
Yalkut Shimoni at the end of Eicha says that the 9th of Av will turn into a day of celebration, as Hashem will Himself rebuild Jerusalem and gather the exiles (see Tehillim 147:2). As the Rebbe of Ishbitze wrote, the month of Aviv (Pesach time) is the father (av) of the months, but the month of Av is even more of a father. In the future when all other holidays will cease, even Aviv will be subsumed under Av.