To enable real time shipping rates from Easyship in your Checkout through Magento 2, please follow the below guide.
This will allow you to shop the Cheapest, Fastest and Recommended shipping solutions for your customers orders in your Store Checkout process.
Please note that you can change or limit the couriers shown at checkout by adding shipping rules.
1) Login to the Magento Admin with an Administrator account.
2) Go to Stores > Configuration > Sales > Shipping Methods > Easyship
3) Enable Easyship in Checkout and set the Base Category. 
Once done, your customers should now see Easyship rates in your Checkout flow!
If the quotes are inaccurate in any way, please make sure that your dimensions and weights are entered accurately for all your products.
