Technically you don't take a damage nerf for being small yourself - being small means you normally use small weapons, and the weapons have a damage nerf due to their size. A medium longsword will do 1d8 damage regardless of whether the wielder is a human, a halfling or an ogre - all you need to do is work out how you're going to use it.
A creature can't make optimum use of a weapon that isn't properly sized for it. A cumulative -2 penalty applies on attack rolls for each size category of difference between the size of its intended wielder and the size of its actual wielder.
The measure of how much effort it takes to use a weapon (whether the weapon is designated as a light, one-handed, or two-handed weapon for a particular wielder) is altered by one step for each size category of difference between the wielder's size and the size of the creature for which the weapon was designed.
So, without any special feats or magic, you can wield a medium longsword as a two-handed weapon, a medium shortsword as a one-handed weapon, or something similar, and get the same damage as a medium character would get from using that weapon (but with a -2 penalty to attack rolls). Unfortunately, between the attack penalty and the increased effort designation, this is generally a bad idea. Before taking the -2 to attack rolls into account, the medium shortsword is essentially a small longsword and the medium longsword is worse than a small greatsword - add in the attack penalty, and they're completely outclassed. (It is worth bearing in mind, though, since you can't always choose exactly the weapon you want. You might find a really awesome magic dagger somewhere, or steal a medium shortsword from the guards who confiscated all your on-size weaponry...)
You can use certain feats and magic to improve this situation further.
Obviously, anything which increases your size will allow you to use weapons of your new size with no penalty (and at least some such effects will also automatically increase the size of any weapons you possess at the time). Dyndrilliac's example of Enlarge Person is an excellent early-access option for this, and things like Alter Self and Polymorph can also change your size category (among other things).
Complete Warrior has the Monkey Grip and Wield Oversized Weapon feats, which allow you to get around the 'oversized weapons take more effort to use' rule and use a medium weapon while still being small, and the Magic Item Compendium has the Strongarm Bracers which do the same thing.
I'd strongly echo Ruut's advice not to worry about it ... but if you want a workaround, those are the options I know of.