Knight isn't much faster than Viking, from what I recall, and while yes, Viking's Weapons are a lot heavier...
They're a lot stronger, which I figured would compensate some. Blessed Hammer is 120 Power, 2 are gotten in Fargabad. Defenders, which are gotten just before the Invincible (so only slightly before) are 96 Power.
To credit of Viking, given they have better armors for a good part of the first world, they can opt for a Feather Helmet more readily, there by negating the speed loss some...actually...lets see their stats!
*Checks*
They have identical speed it looks like (26 at level 50, 45 at level 99), and Vikings have higher Strength (50 at level 50 vs. Knight's 45, 99 at level 99 vs. Knight's 86;), which is effectively +that much Power to each hand.
At Amur (when you first get Viking), the weapons in question are...
Knight: Royal Sword (50) + Blood Sword (55)
Viking: Battle Axe (65)x2, gets Hammer in dungeon which is 55 Power and Thunder elemental
Admittedly, hits matter A LOT more this early, so yeah, Knight probably wins? Also has better accuracy.
In Saronia, Knight's still using the same stuff. Viking gets a single Dragon Hammer (70 Power, Thunder Elemental)
After Undersea Cavern (should be done first since easiest of underwater dungeons w/ good rewards that help in Temple of Time...a lot. Odin could be argued first, but both get only defensive benefits anyway)...
Viking: Dual Tomahawk (73) + Triton Hammer (110 Power, Thunder Elemental)
Knight: Blood Sword (55) + Ancient Sword (86)
Can't...honestly see Knight beating Viking here. That attack difference is too dramatic. Post Temple of Time, Knight gets rid of that Blood Sword in exchange for a Defender (95 Power), which probably shifts things around again. I think you get a second Defender in Ancient Ruins, whether its store bought or found, dunno; I know that they're store bought on the INvincible at the latest.
On Invincible, Viking can upgrade to Rune Axe (110 Attack), or you know, not waste the money, and go to Fargabad where he can get Demon Axe (116 Attack, +3 Strength; note that strength boosts function like Attack boosts, but they work on both weapons, so +3 Strength with 2 weapons is like +6 net attack in practice, meaning 2 Demon Axes becomes effectively 122 Power each, if that makes sense), or even better, don't buy them, save money, and get those 2 Free Blessed Hammers (120, Lightning Elemental) instead.
Viking's kind of stop upgrading, Dual Haken (122, +3 Strength) in the Labyrinth aside. Knight...well, not only does it get Break Blade, but also both of the Eurekan Swords, so it obivously kicks Viking's ass post Eureka; no one ever denied that I don't think.
So yeah, that's the weapon comparison throughout the game. I left out a few weapons here and there, but they're all pretty much Obsolete Viking Stuff (like those 115 power hammers gotten in Leviathan's Dungeon, which are useless since Blessed Hammers are better and gotten at the same time)
You are right that Vikings have a disadvantage in JLevels off the bat, though, Knight isn't around THAT much longer than Viking (2 dungeons and some over world), and after JL14, Vikings have faster Job Level growth (14 per action compared to 12), so they can catch up pretty conceivably.
Also, because Viking Mail kicks the shit out of Knight Armor, Vikings can opt for Feather Helmet more readily than Knight's Can, thus gaining that +2 Agility, though, Knights can still use this of course, just tossing the option out there...
...then again, I think Knight's LACK a better helmet at that point in the game so they'll be using it anyway, so moot point; non-Class Specific Armor really sucked at that point, hence why Dark Knight's are so frail at that point. Also worth noting that Knight Armor is worse than what Bard's and Geomancer's get <_< >_>