Short version: 2x4's are made out of light strong wood.

Construction lumber (2x4 2x6 etc) is typically made out of Spruce, Pine, or Fir, often abbreviated as SPF, or "whitewood" which can be just about anything cheap including SPF. SPF are rather high on the strength to weight ratios as it is and you're not likely to find an easy source of lighter wood as strong. If you have access to good woodworking equipment you might have luck thinning down a 2x4 or 2x3 to the size you need but still get the required strength. You could also go with the 3/4" thick whitewood sanded boards the big box stores sell to save on some weight in places, but be careful you get enough strength. It can be significantly more expensive that way depending on the dimensions of the boards you choose.

Getting the strength you need and having it as light as possible is going to come down to your design skills in the end.