A quick search on google revealed many luggage storage facilities in Osaka. IMHO it would make sense to leave the luggage in the station/airport from which you would be departing/returning when heading/coming back from Tokyo.
To this purpose, here is a page detailing how to access the luggage storage facility at Shin-Osaka station, for a cost (at the time of writing) of 410
JPY per day, until the 5th day after which the price becomes 820
Outside the Southern Shinkansen Gate at Shin-Osaka (which puts you on the 3rd floor of the station – see map but it won’t show the luggage room) you will go down two more floors to First Floor to get to the bus pickup. At the bottom of the steps to 1F turn left to see Central Gate and the bus and car area outside, as well as some bicycle parking just past a convenience store. Go left on the other side of that convenience store and you can see the luggage storage at the end of the walk up a short ramp for your suitcase’s rollers.
JR-Osaka station has both coin-operated lockers on 1st and 3rd floor, as well as a manned luggage storage room. Here is the information page from the station website, and here is its google translate version in English. Here is a map of the station in English. Note that coin-operated lockers are emptied regularly by staff, so you might have a maximum storage time of around 48-72h.
I could not find any official information on prices. I did however find this thread on a tripadvisor forum mentioning
they charge you 400 or 500yens per suitcase per day.
Kansai International Airport
Kansai International Airport also has a luggage storage facility. The liked page mentions carry-on baggage storage, and your 15kg should fit this criteria:
There are temporary storage facilities for carry-on baggage at the northern and southern ends of the 1st and 4Fs. The northern counters are operated by Kansai Airport Baggage Service, and the southern counters are operated by JAL ABC.
It is 620 yen to leave a suitcase for one day, 360 yen for a Boston bag, 1,030 yen to leave a coat for 4 days or less (from the 5th day, 210 yen is added per day), and large items such as surfboards may be left for 1,030 yen a day.