I agree the "legal" argument is not valid.
For good reasons juries are prevented from hearing weak evidence. The duty a jury is charged with is making a beyond a reasonable doubt decision and evidence that is only weak is not substantially probative with regard to that kind of decision.
However, that is not the kind of issue here. The issue here is to determine roughly the likelihood and nature of an HJ. Even weak evidence can be evaluated for the possibility that it might suggest a possibility or that it might be stronger or weaker than it is generally assumed to be.
What weak evidence of Jesus of Nazareth in the NT are you talking about? Where is it? Is it in Philo, Josephus, Tacitus, Suetonius, Pliny the elder, Pliny the younger.....?
We have statements about characters in the NT like John the Baptist, Pontius Pilate, King Herod, Tiberius the Emperor, Festus, Agrippa, Bernice, Caiaphas and these characters are found in non-apologetic sources.
There is no evidence at all for a character called Jesus of Nazareth by any contemporary non-apologetic writer of antiquity.