The Rashbam to Bereishis 43:33 writes that not only were the 6 sons of Leah born in 7 years, but also all of the other sons of Yaakov (with the obvious exception of Binyamin, who is explicitly mentioned as having been born later).
There are two basic possibilities of how this would happen. One option is that the literal chronology of the verses (which implies that each pregnancy only began after the previous pregnancy ended, and not that pregnancies overlapped where applicable) is not meant to be taken literally, and when Yehuda was born, Bilhah was already well into her pregnancy with Dan etc., which frees up (let's say) 2 and a half years or so which are accounted for by overlapping pregnancies.
The other option is that each pregnancy began very shortly after the previous one ended, and that most if not all of the sons of Yaakov were born at 7 months. This would not be incredibly strange, as we have a fairly large cast of significant Biblical characters who were born at 7 months, or into the 7th month (including Yitzchok (Rosh Hashana 11a), Peretz and Zerach (Rashi to Bereishis 38:27), Moshe Rabbeinu (Rashi Shemos 2:3) and Shmuel (Niddah 38b), among others). This would yield 12 pregnancies at 7 months each = 84 months of pregnancy over the course of 7 years = 84 months.
רבינו בחיי in Parshas Vayishlach (Bereishis 35:30) writes that Reuven, Shimon, and Levi were all born at 7 months. מחזור ויטרי to Avos 5:21 writes the same. The reason they only identify these three is that by them it is implicit in Chazal, as they say (Bereishis Rabba 80:10) that Levi was 13 when he and Shimon attacked Shechem, and if you do the math (I'll leave it to the reader) this means he had to be born within less than 2 years of Yaakov's marriage to Leah. Once we know the first three had this "incredible coincidence" of all being born at 7 months, I see no reason to assume that a) there wasn't some hashgacha-related significance to that which would carry through to the rest of the children of Yaakov, and b) that there wasn't some biological condition that Leah had, and by association her sister(s) (as there is evidence that preterm labor has genetic factors), which made them prone to preterm labor.
However, the Ralbag, due to other problems in working out the chronology of the birth of Yehuda's children, understands this story very differently (bottom of second column in link). He says that really Yaakov married Leah and Rachel at the beginning of the first 7 years, not at the end. He concludes that this resolves another issue of how 12 children were born in 7 years, as according to his explanation it was 14 years. He concedes, however, that the verses in their simple reading imply both of my above assumptions, that it took place in 7 years and they were all consecutive without overlap. He also notes that the view of Chazal is not in accordance with his own view. [I would also note that this is exactly the kind of thing that the Maharal raged against the Ralbag for - extricating the verses from both their simple meaning and the way Chazal understood them to satisfy his own notions.]