In the main rulebook, there is no real description of what bracing actually does outside of heavy weaponry. However, in the IH you can give tripods and bipods to basic weapons and their only use is to assist with bracing.

So my question is, is there any effect from bracing basic weapons? It seemed like no to me.

In my game I grant a +10 bonus to hit when bracing a basic weapon

I basically assume that aim-action (half or full round) means that the character is using any available bracing and/or dropping to kneeling or prone shooting position to steady the weapon. Thus I also assume that the bracing bonus is already calculated into the bonus for aim action.

However, if you wish to introduce a separate bonus I'd say +10 for bracing weapon or taking prone shooting position (equal to bracing weapon to ground) is quite okay and would take half-action to accomplish.

Also, although rare, there are some basic weapons that have Str minimum that can be circumvented by bracing.