In simplest terms, the primary cause of weather helm is the center of effort (CE) of the sail plan being farther aft than it should be. Other factors, such as heel, also lead to weather helm, but moving the CE forward will address the secondary causes as well. Here are two simple fixes for the range of wind speeds you mentioned.
The first is to reef the mainsail. Wind force aft of the mast, is trying to turn your boat up into the wind like a weathervane. Reducing mainsail area will reduce that force. The CE of a reefed mainsail is forward of (and lower than) the CE of a full mainsail, so reefing the mainsail moves the CE of your overall sailplan forward. Lowering the CE reduces heel which improves the symmetry of the hull shape underwater. Racing crews and dinghy sailors typically don't reef as readily as cruising sailors do because they can hike out to help keep the boat flat. Less heel also means less drag, which makes the boat faster.
The second thing you can do is reduce the headsail area to the size of a working jib (100% or 110% jib). It may sound odd because you would think that increasing the headsail size would move its CE forward. However, a large headsail like the popular 150% genoa has a THIRD of its area aft of the mast, where it doesn't help. A 110% jib has its area and its CE forward of the mast to do the most good when the wind picks up.
Frankly speaking, reducing sail when the wind builds is inconvenient. Even with a roller-reefing headsail, both genoa cars have to be repositioned to maintain the proper sheeting angle. However, turning upwind in a 15 kt breeze can double the speed of the apparent wind and quadruple its influence on the sails, rig, boat and crew. Setting up the rig to make reefing simple and trouble-free will pay huge dividends.
By the way, weather helm can be reduced by using sail trim, but its not as universally applicable as reefing nor as worry-free. It also requires investing in more boat part$....
