If you're not worried about throwing out your elbows (which is an undeniable risk here), you need to identify what weight range you think your classified under. Wrist weights generally don't come above fifteen pounds, though I'm sure there are exceptions. Dumbbells as I'm sure you know, come in a very wide range of weights, and therefor, if you need thirty to forty on your arm (Lord forbid) would be a better choice.
Also with the increase in weight is the increasing danger to the tissues that support your limbs: keep that in mind.
Another option is a weighted punching bag, whose force goes against the direction of your arm, making it safer, and if done right, more effective.
Option number four, especially if you really can't lift much, is to strap wrist weights to your upper arm, reducing the risk of injury, though working on a completely different muscle set.: Don't rule this one out, even if you can take a lot of weight, as any motion done in repetition can build strength.
For boxing, if your legs are really your best pieces, try kind of 'springing' up from the ground, and making sure you let your motion flow out of your legs, having your arm only channel it.
Building strength is usually about just pushing yourself until you can't anymore, no matter what method you use.