ex –
city (colombo 1 – 10) on full cart weight 1st kg Rs. 100 and each additional kg Rs 50 ……
city (Kandy) on full cart weight 1st kg Rs. 200 and each additional kg Rs.50 ……
city (galle) on full cart weight 1st kg Rs. 100 and each additional kg Rs. 50 ……
i want to go by city let customer to select nearest city from drop down . no postal code request. Calculate shipping base on city and weight. please help me how can i do this

if some one buy 2 or 3 product worth of Rs.1000/=
and if he select city as Kandy
and if cart wait is 2.5 kg

customer product cost 1000/=
shipping (kandy) Rs300/=(since Kandy base rate is 200 and additional KG is Rs.50)
(2.5 kg – 1kg Rs.200 +Rs50 +Rs50=300)
total price = Rs 1300/=

please help me to know how to do this

This tutorial describes how to set up shipping by weight and includes the php snippet you’ll need
https://businessbloomer.com/woocommerce-shipping-weight-without-plugin/

I hope that help!