Instead of having to work on both the anime and the manga at the same time, why don't the authors just focus on one?
For this answer I am going to assume only works which began as an anime and were later adapted into manga are under consideration. This is hard to study nowadays because there are so few anime-original works, but in most of the cases I know of, the manga is just tie-in merchandise for the anime, the same way anime adaptations of manga are tie-in merchandise for the manga, or anime and manga adaptations of light novels and visual novels are tie-in merchandise for the light/visual novel.
Usually, the author of the manga is a contract worker of some sort: the studio hires them to write and draw a manga version of the anime, sometimes while the production of the anime is underway, and sometimes after it's finished. The original team behind the anime doesn't usually work on the manga; their names might be on the cover as a "Story" credit, meaning they're just being acknowledged as the creator of the story. It's the reverse version of seeing "Based on the manga by XX" in the opening credits of an anime. So having a manga adaptation doesn't actually take any effort away from the anime; the two productions go ahead independently, sometimes extremely so. For example, the first manga adaptation of The Vision of Escaflowne was based on an early version of the story from when Yasuhiro Imagawa was attached as director. Imagawa left to direct G Gundam and the production was put on hold, but the manga went ahead with his shounen version of the story, only to become inaccurate later when Kazuki Akane came in and reworked the show as a shoujo series.
Some anime also have spinoff manga, which aren't directly based on the original anime. Evangelion, for example, has Angelic Days, Shinji Ikari Raising Project, and Campus Apocalypse. Madoka has Kazumi Magica, Oriko Magica, Wraith Arc, The Different Story, Homura Tamura, Homura's Revenge, Tart Magica, Suzune Magica, and probably soon the epic crossover Puella Magi Mahoro Magica: The Resurrection. Like the direct adaptation manga, these are passed off to hired help, but they often have valid creative reasons for existing. Angelic Days and Shinji Ikari Raising Project explored the banal world that Shinji creates in his mind in Episode 26 of the anime. Wraith Arc and The Different Story fill in parts of the anime storyline that weren't shown onscreen; Suzune Magica and Tart Magica focus on different characters in the same world; Homura Tamura is a parody. Since manga are cheaper to produce than anime, the spinoff manga are a low-cost way to explore the world of an anime, or create alternative scenarios, or to give hardcore fans something they want that doesn't have wide enough appeal to fund another anime. Some of these spinoff manga, I don't care about, but reading The Different Story totally changed my view of certain characters and events in the anime series, so I'm glad that the anime staff didn't decide to "just focus on one" and allowed the spinoff manga to be made.
Like @ToshinouKyouko and @JonLin commented, there is more money to be made, while the author don't even have to lift a finger. So, as a working person, why not? You get a chance to earn more with very little, if any, work to do.
Sword Art Online
I'll take SAO as an example. Volume 14 of Sword Art Online (SAO) was sold at 590 JPY per copy and 350,693 copies was sold in 2014 fiscal year (November 18, 2013 - November 16, 2014). The total income for the publisher would be 206,908,870. Sources here and here stated that the average royalty rate for a writer is between 8% to 50%. I didn't manage to find a reference for the Japanese publishing companies. So, let's assume that the royalty is at 10%, Kawahara Reki (SAO's author) would earn 20,690,887 JPY from volume 14 alone. SAO got 3 volumes released per year. Assuming that every volume sold at the same price and number, per year Kawahara-sensei would receive 62,072,661 JPY from the LN alone.
Sword Art Online also has anime adaptation. It was being sold on DVD and BluRay (BR) for 5,800 JPY and 6,800 JPY respectively for the first volume (episode 1 and 2 of first season). Next volumes sold for 6,800 JPY and 7800 JPY respectively. 17,677 copies of the first volume of the second season got sold in a week between 2014 November 10 and 2014 November 16. Volume 1 of the second season of SAO was sold at 6,800 JPY for DVD and 7,800 JPY for BR. It was release on 2014 October 22, that is 3 weeks before. Assuming it gets sold at the same amount for every week, then we get 53,031 copies sold for the first 3 weeks. Total income from BR sells would be 413,641,800 JPY.
Cost per episode is approximated at 15,000,000 JPY per episode (DVD and BR printing cost included). The aforementioned SAO season 2 volume 1 BR has 3 episodes in it, thus it cost about 45,000,000 JPY. The creator got 1.7% of the net revenue (income - production cost), that is 6,266,910.6 JPY (1.7% x 368,641,800). Like I mentioned earlier above, the creator don't have to lift a finger to get that extra income. The anime production house would take care of it. They have a scenario writer and director to make the anime based on the LN.
Now, a LN release only 3 volumes a year, but BR releases 1 volume per month, that is 12 volumes a year. SAO II may only have 9 volumes, but that is still 9 x 6,266,910.6 JPY (56,402,195.4 JPY).
- The KonoSuba LN selling went up after the TV anime aired by approximately 3 times.
- I assume Kawahara-sensei's contract earns him royalty at 10% rate. Since he is a best seller, it is possible that his contract earns him more than that rate.
Generally, when an anime is being produced there is a studio doing the production. There are numerous writers/editors working on it and the author may or may not have creative control of the content.
I would say the work involved also depends on the source material in question. There can be both licensing for an anime and a manga to be produced simultaneously from something like a light novel.
There is also the fact that anime, airing on TV, is subject to stricter guidelines in content. Particularly in regards to violence and nudity.