Question: The Bible often speaks against following tradition more than the Word of God. The martyrdom, however, of almost all of the apostles is known to us because of tradition. My question is, why do we give this tradition more weight than other traditions?
Response: You rightly point out that tradition can never be given the weight that Scripture has. Because of this, you wonder why "we" give the tradition concerning the martyrdom of the disciples more weight than other traditions.
We don't. On the extremely few times we would reference the "traditions" concerning the death of the apostles, we should point out that they are just that, only traditions. Consequently, if we say "traditions," our readers should recognize that this does not carry the weight of Scripture, and should be treated as such.
Further, the tradition regarding the martyrdom of the Apostles is used in clarifying history, not in formulating doctrines as the traditions of Catholicism are used. That's a vast difference.
Moreover, in the Scriptures we are given glimpses of the martyrdom the Apostles would endure. Paul, from his prison cell in Rome wrote, "For I am now ready to be offered, and the time of my departure is at hand" (2 Tm 4:6). Jesus told Peter, "Verily, verily, I say unto thee, When thou wast young, thou girdest thyself, and walkedst whither thou wouldest: but when thou shalt be old, thou shalt stretch forth thy hands, and another shall gird thee, and carry thee whither thou wouldest not. This spake he, signifying by what death he should glorify God. And when he had spoken this, he said to him, Follow me" (Jn:21:18-19). Where wouldn't Peter previously go?
In John:13:36-38 we read, "Simon Peter said unto him, Lord, whither goest thou? Jesus answered him, Whither I go, thou canst not follow me now; but thou shalt follow me afterwards. Peter said unto him, Lord, why cannot I follow thee now? I will lay down my life for thy sake. Jesus answered him, Wilt thou lay down thy life for my sake? Verily, verily, I say unto thee, the cock shall not crow, till thou hast denied me thrice."
Peter wouldn't go all the way to the cross. Tradition holds that Peter was crucified upside down on a cross. The words used in Scripture would seem to support this scenario, but one cannot be dogmatic about the tradition, although it may seem "plausible."