Because Game Freak made it that way.
Game Freak makes the Pokémon, so Game Freak makes their base stats. If Game Freak wanted to give one of the new starters, like Pombon 670 BST, they could do that, because they are the ones who make the Pokémon.
{Accurate Leak from a reliable source}
If I had to guess as to why Game Freak gave Slaking 670 BST, it's probably because Gen III, the generation in which Slaking was introduced, also introduced abilities, so they probably thought it would be a cool idea to have a Pokémon with amazing BST but had an awful ability to compensate. They have also used this idea with other Pokémon, like Regigigas.
However, I don't think you wanted a "Game Freak Logic" answer. If what you mean is: "How on Earth is Slaking balanced?" then the answer is simple. Slaking's only option for an ability is Truant, which is the WORST ABILITY EVER. It's even worse than Slow Start, because at least Slow Start wears off after 5 turns. With Truant, you miss out on every other turn, meaning that your opponent can attack twice as often as you, and you can't attack every other turn.
The only "benefit" of Truant is that moves that require you to recharge afterwards, like Hyper Beam or Giga Impact have no downside, because Slaking can't attack afterwards anyway. I type "benefit" like that because it isn't really a benefit, it just makes all moves into Hyper Beam, meaning that Hyper Beam itself has no drawback.
As for your Weezing strategy, Neutralizing Gas teams already exist, so looking up one for the format you plan on using this in, and it could help you build a team around this strategy.
Hope I helped.
