I am surprised no one has really mentioned this yet, but I have some thought concerning the weaponry and the fights between Beowulf and Grendel, and then again with Grendel's mom. Grendel had already declared that he does not fight with a weapon, thus, I believe is why Beowulf enters the fight also without a weapon. This is one of the oldest traditions and no one has brought it up. When entering a one on one fight, the two opponents come with equal weaponry. Old westerns: each gun-slinger has one gun, sword fights- only one sword. Or, on the other side, a wave displays no weapon, so does a handshake. Even sumo wrestlers slap their thighs and wear their minimal mawashi (the 'uniform') to show they do not have any weapons. Furthermore, in the movies we notice the incredible immorality and, essentially, cheating when the 'bad guy' draws out a hidden knife or gun, etc.
So, as far as weapons are concerned- it is as simple as that as to why Beowulf fought Grendel without "help." When he enters the fight with Grendel's mother, he does not know what exact weapon she may bare.
So there it is: in a true and fair fight, only experience, knowledge, and strength are to be the variables.