I had a few minutes to look at the Rosh on Kidushin page 64b. [One of the major poskim (people that wrote on the Talmud from the standpoint of determining the law--as different from people that wrote on it with a view to explain the difficulties) of the Middle Ages.] And I see that I need to do a lot more work on that subject there because there seems to be a debate among the rishonim how to understand that subject. You have Rashi and the Baal Hameor [Rav Zarahia HaLevi] on one side. On the other you have the Rosh and the Ramban.
Still from what I could see my answer for R. Akiva Eiger still looks valid -- at least if you look at the subject from the viewpoint of Rashi. [I might mention here that I have heard this before when I was at the Mir in NY--that often the questions of R Akiva Eiger are only to one opinion. Just switching to the other opinions will often answer the question. So you have to assume he was asking his question according to the viewpoint of the alternative opinion. I actually had that experience once while at the Mir. In those days it was the custom for young married men to give a kind of informal class that was separate from the regular scheduled classes. I was giving such a class there and in fact discovered that a question of R Akiva Eiger in Shabat could be answered based on a Tur in the laws of festivals.]
So just to make this short: The Gemara in Bava Batra [if memory serves me correctly] asks why do you need an extra mishna to tell us if the husband says before he dies "I have a son" he is believed. If he says "I have a brother" he is not. Answer: the Mishna is telling us even when there is a Hazaka (prior status) that there is a brother. [What this seems to mean (at least the way Rashi and the Baal HaMeor understand it) is that he says also I have a son. So when he says "I have brother" and there is also a Hazaka (prior status) that there is a brother she is still permitted to marry someone without Yibum. [Yibum is when a woman is married and her husband dies without seed, she has to marry his brother. --or do Haliza (taking off the sandal) as mentioned in the Torah.]
R Akiva Eiger asks right there why does the gemara say a hazaka. Even with witnesses she also should be allowed to marry without Yibum.[It seems to me clear in any case that R Akiva Eiger is asking only according to the opinion of the baal Hameor since to the other opinion his question would not make sense.]
My answer is based on Kidushin 64 that wants the Mishna to be like R. Nathan not just R Yehuda Hanasi.
The point is over there in Kidushin R Nathan goes with Hazaka (prior status) if he says "I have a brother" to believe him to make her forbidden to remarry without yibum. But if he also says I have a son she is permitted. But my point is that if there would be more than a Hazaka but also witnesses, then R Nathan would say no.--and forbid her unless there was some evidence that there is a son.
And just by taking a quick look at Rashi and the Rosh today I saw that this answer is very clear in Rashi since Rashi says that if a brother would come later and say that he is the brother then he would not be believed. But from that Rashi you can see that if there would be witnesses at the time she wants to be permitted to remarry then we would need evidence that there is a son.
I also had another proof for this answer but I forgot it.
Still from what I could see my answer for R. Akiva Eiger still looks valid -- at least if you look at the subject from the viewpoint of Rashi. [I might mention here that I have heard this before when I was at the Mir in NY--that often the questions of R Akiva Eiger are only to one opinion. Just switching to the other opinions will often answer the question. So you have to assume he was asking his question according to the viewpoint of the alternative opinion. I actually had that experience once while at the Mir. In those days it was the custom for young married men to give a kind of informal class that was separate from the regular scheduled classes. I was giving such a class there and in fact discovered that a question of R Akiva Eiger in Shabat could be answered based on a Tur in the laws of festivals.]
So just to make this short: The Gemara in Bava Batra [if memory serves me correctly] asks why do you need an extra mishna to tell us if the husband says before he dies "I have a son" he is believed. If he says "I have a brother" he is not. Answer: the Mishna is telling us even when there is a Hazaka (prior status) that there is a brother. [What this seems to mean (at least the way Rashi and the Baal HaMeor understand it) is that he says also I have a son. So when he says "I have brother" and there is also a Hazaka (prior status) that there is a brother she is still permitted to marry someone without Yibum. [Yibum is when a woman is married and her husband dies without seed, she has to marry his brother. --or do Haliza (taking off the sandal) as mentioned in the Torah.]
R Akiva Eiger asks right there why does the gemara say a hazaka. Even with witnesses she also should be allowed to marry without Yibum.[It seems to me clear in any case that R Akiva Eiger is asking only according to the opinion of the baal Hameor since to the other opinion his question would not make sense.]
My answer is based on Kidushin 64 that wants the Mishna to be like R. Nathan not just R Yehuda Hanasi.
The point is over there in Kidushin R Nathan goes with Hazaka (prior status) if he says "I have a brother" to believe him to make her forbidden to remarry without yibum. But if he also says I have a son she is permitted. But my point is that if there would be more than a Hazaka but also witnesses, then R Nathan would say no.--and forbid her unless there was some evidence that there is a son.
And just by taking a quick look at Rashi and the Rosh today I saw that this answer is very clear in Rashi since Rashi says that if a brother would come later and say that he is the brother then he would not be believed. But from that Rashi you can see that if there would be witnesses at the time she wants to be permitted to remarry then we would need evidence that there is a son.
I also had another proof for this answer but I forgot it.