14 day japan itinerary

I am going to Japan for 2 weeks on May 14-May 27. I am arriving in Hanade airport at 12pm. I have a few places that I want to go to:

Tokyo (4nights),
- Ryogoku Sumo Town
Chankotomoegata
- Tokyo Skytree
- Akihabara
-Maidreamin�f
- Shibuya Pedestrian Scramble
- Meiji Jingu Shribe
- Harajuku Takeshita-Dori
-Cafe & Pancake Gram
-Han No Daidokoro
- Asakusa
- Senso-ji Temple
- Ueno Park
-MarioKart tour
- The Tsukiji Market
- Tokyo Tower
- Rainbow Bridge
-Shinjuku Gyoen
-Bitter Sweet
- Robot Restaurant

Kyoto (3 nights),
- Gion (entertainment district)
Kagizen [Tea room]
- Kyoto tower
- Arayashima bamboo forest
- Ryoan-Ji
- Kinkakuji Temple
-Nishiki market
- Fushimi Inari-taisha Shrine
- Kiyomizudera Temple
- Kyoto Imperial Palace

Osaka (3 nights),
- Osaka Castle
- Umeda Sky Building/Floating Garden Observatory
-Okonomiyaki Kiji
- Universal Studios
- Sumiyoshi Taisha Shrine
- Dotonbori & Glico Running Man Sign

Mt Fuji tour (day trip)


What itinerary can you suggest?

What will be the weather in Japan in the middle of May?

You just listed your itinerary - so why do you ask for one?

A few observations though - if you are going to the Sky Tree, then the Tokyo Tower is rather redundant. If you will go to Tsukiji and want the tour, you'll need to be there around 4 AM or before to sign up. If you are not staying nearby, you'll need a taxi to get there.
For Kyoto, there is no point in going all the way to Arashiyama just for the Bamboo Grove
https://youtu.be/JaQuRm38G94
which you'll be finished with in just 20 minutes. It does make one part of a half day or day at Arashiyama though, with other sights like the Iwatayama Monkey Park, Tenryuji, the Otagi Nenbutsuji Temple, etc.
https://goo.gl/Neiowd
Fushimi Inari is open 24/7, so it's easy to fit in the evening or early morning and you can also avoid the crowds.
I also recommend taking half a day off of Osaka and seeing Nara as well. It too was a former capital and has some of Japan's best sights. Skipping the Todaiji Great Buddha would be a tragedy.
http://bit.ly/1Rhxg0E
For Dotonbori and the Umeda Sky Bldg, the ideal time to go would be in the evening, or for the latter, right before sunset to see the city change from day to night. USJ will pretty much take up a whole day. I can't see the logic in flying all the way to Japan to go to an American theme park, and then wait hours in line for 3 minute rides, but it's your time.
For the Mt Fuji area, you need to specify if you want to see the Hakone area of the Fuji 5 Lakes area.
http://www.japan-guide.com/e/e5200.html
http://www.japan-guide.com/e/e6900.html
There are regional passes for both areas.
http://www.odakyu.jp/english/deels/
Weather in mid-May is generally pretty good. Not too hot or cold, but with spring arriving early, you could get some humid days and there are always some days spoiled by rain. You should have a back up plan just in case (museums and aquariums are a few options).
If you're going from Tokyo to Kansai and back within 7 days, then the japanican ticket is one of the best bargains you can find.
https://www.japanican.com/en/tour/detail/PAS1J02031MKC/

As you are already spending quite some time in urban areas like Tokyo and even Kyoto, maybe skip Osaka and visit the Japanese countryside instead?