That 'little bit' of extra damage actually increases damage done by 10x, so it can be very useful if the crit spot spawned in good place.
There are a few good ways to solo hardsuits which I've used with success:
Flamethrower: Quickly kills the pilot, leaving the hardsuit free for someone else to take. This is a mixed bag, as while it is a quick kill, you need to be able to get close enough to the enemy to use the flamethrower due to its limited range. This doesn't destroy the suit, either, so if you get fragged right after you kill the pilot, his teammates are free to start using it again. On the other hand, this can mean a free hardsuit for you, too. Getting close to the suit can be rendered trivial if you've got Cloak and pretty much becomes a free kill at that point.
Armor Stinger: Two shots from a stinger will blow a hardsuit up. The stinger is handy because you can engage the hardsuit from a long distance. The downside to the stinger is that after the first rocket, you need to reload before you can fire the second. This generally requires thinking ahead as you need to find an obstacle to duck behind and reload so the hardsuit doesn't kill you when it turns around to figure out where the rocket that hit it just came from. While the range the stinger has is certainly an advantage over the Flamethrower, this also makes it more likely to miss your target, or miss an opportunity if the suit boosts around a corner, etc. Much safer than a Flamethrower, but a lesser chance of disabling your target.
Bullets!: This is my preferred method of dealing with suits, but this method generally needs a prerequisite or two. The first thing you need is a gun that does enough damage, fires fast enough, and has enough bullets to take down all of that health. This pretty much means the LMG, or LMGR. The second thing is a well-placed crit spot on the suit; small crit spot on the front == very risky, big crit spot on the back == easy target. The hardsuits turn slowly enough to where if you get the jump on them from behind and start nailing their crit spot, you stand a pretty good chance of downing them with a gun that meets the prior requirement. There are ways to make this method easier, too. Things like stun mines, shock grenades, shock bullets, and (my favourite) EMP grenades. EMP the suit, run in with your LMG, blast the crit spot, and you can destroy it before it comes back online. This, like the stinger, also destroys the suit.
Breach Hammer: The Breach Hammer plays by special rules when it comes to the hardsuit -- the damage done is increased by more than 10x if you hit the weak spot. If you're able to hit the spot twice with the hammer, it will destroy the suit. This can be one of the most difficult methods because it requires you to be in melee range and that the weak spot spawns in a 'good' place; if it's on the upper leg, you're very likely to hit one of the arms instead, and if it's on the front, you're very likely to get shot instead. From personal experience, spots on the back or lower arms seem to be relatively easy.
The Barricade can be handy tool (yet not a full-fledged strategy) for hardsuit encounters whether you're fleeing or trying to engage
because the rail gun won't even hurt you if it hits it. This has recently been changed, the Barricade doesn't stop rail gun damage any longer. As you get closer, you become more likely to die of machine gun spread, so I don't recommend trying to get close for a Flamethrower kill with this.