If flying via Precision from Kenya to Zanzibar, believe the weight limit is 20Kg/44-lbs as this is considered an International Flight. Please though reconfirm with Precision (should be on their web site) that this is so.
On arrival at Wilson from the Mara at about 12:15pm you'll have to transfer thru horiffic NBO traffic to the NBO/JKIA international airport for the Precision flight and as an int'l flight, minimum 2/hrs prior departure. However, a thread above indicates that since the first at JKIA, they'd prefer you allow 3/hrs prior departure to clear checkin/security.
Best to leave what you'll be taking to ZNZ with your tour operator who should bring it to Wilson for you to continue onto JKIA. I can't honestly advise whether there is secured storage at Wilson... sorry.
Remember, you will not only require Visa for Tanzania/Zanzibar that can be purchased on arrival, and most definitely a Yellow Fever inoculation and proof of same for entry to the island.