When purchasing  heat shrink bands You should be aiming for  bands that are large enough to fit yet are within a few mm of to the true lid diameter size you require -
 

If your jam jars require a  63mm jar lids  it means the screw thread  is 63mm  
However this is not a true indicator of the outside diameter of the lids - in most cases the true diameter of the lid will be a few mm larger 
EXAMPLE 
A metal lid sold as a 63mm  jam jar lid will have a  true lid outside diameter of  around 66mm 
The listed bands I sell for 63mm jam jar lids will fit a max of 69mm diameter.

Each  size of shrink Band  has a max size in the listing 

  
Always measure the  true max diameter of your lid.
Diameter is from side to side ,outside edge to outside edge , all the way across if you have one please use a vernier Caliper.
Please note tamper evident heat shrink bands cant be stretched in any way

Match your true lid  measurement  with the closest max band size ---this  must be less than the true lid diameter