I agree about keeping the box reasonably light, but my reason is to make it easier to handle. I hope that a light box will be treated more carefully than a heavy one. The items I suggested loading in the box do not add much weight.
The rules are covered in the airlines "Contract of Carriage". You can get these from the airlines websites. Sometimes they are a bit ambiguous. I would recommend you are familiar with the Contract of Carriage for your airline as i) ticket agents usually are not and often tell you erroneous information ii) to help resolve any issues with a gate agent.
For SWA their website says:
Non-motorized Bicycles, including Bike Friday and Co-Pilot, will be accepted in substitution of a free piece of checked baggage at no additional charge provided the bicycle is properly packaged and the box containing the bicycle fits within the 62-inch sizing limit and weighs 50 lbs or less . (Maximum weight is 50 pounds and maximum size is 62 inches (length + width + height) per checked piece of luggage). The handlebars, kickstand, and pedals must be removed and placed inside the box. A $50.00 each-way charge applies to bicycles that don’t meet the above criteria. Bicycles packaged in a cardboard box or soft-sided case will be transported as a conditionally accepted item.
The contract of carriage in section 7(g) makes an exception for bicycles:
g. Special Items
The items listed below shall be acceptable for Carriage as Checked Baggage upon the Passenger's compliance with the special packing requirements and payment of the applicable One-way charge.
Bicycle (defined as nonmotorized and having a single seat) properly packed in a bicycle box or hardsided case larger than 62 inches in total dimensions will be accepted as Checked Baggage. Pedals and handlebars must be removed and packaged in protective materials so as not to be damaged by or cause damage to other Baggage. Bicycles packaged in cardboard or softsided cases will be transported as conditionally accepted items as outlined in Section 7h.
We used to check the remainder in a cardboard box, but now as I mentioned we carry it on. I feel it is one less thing for the airlines to lose. I have done box/carry on method I outlined many times (10 times post 9/11) without difficulty, other than a damaged bike 1x, and two lost bikes 1x. The lost bikes were found after two hours. The location of the lost bikes was resolved in part because I had seen them loaded on the plane, I think it is worth watching from the gate. My only concern with this method would be the carry on size restrictions and your ability to meet them (or slide by). For SWA this is
Southwest Airlines limits carryon bag dimensions to 10x16x24 inches.
IMO this is the best argument for the extra box/suitcase method, but it has never been an issue for us. As a back up you likely could gate check your panniers, but on some airlines their will be an additional charge. We have never had to do this.
Wearing your helmet on is a great conversation starter with passengers, TSA, etc. It explains why you are appear a bit odd, and people generally respect/admire/envy you for your adventure.
A box that is a bit bigger will make a large difference in how hard it is to pack. For example uline has a 56x10x32 box, http://www.uline.com/Product/Detail/S-15111/Corrugated-Boxes-200-Test/56-x-10-x-32-FOL-Side-Loading-Corrugated-Boxes-275-lb-test
They are a bit pricey considering the minimum order and shipping, but it is a nice size. Be aware that some airlines have an upper limit on L+H+W. The upper limits I have seen are in the range of 109-114 inches. SWA does not appear to state an upper limit for bicycles.
Here are some examples of the bike in the box. The wider box makes it a bit easier on the front wheel. Note the home made wooden spreader through the front wheel, the fork spreader, and the removed rear derailleur.