Vector images from AI have totally different stroke sizes

Your When Scaling: preferences have been set to Adjust Scaling Percentage instead of Apply to Content.

That's why you have the same stroke size appearing so differently.  

To fix current art, select all and choose Reset Scale to 100% in the far upper right application menu. That will set the lines to show their true weights. You will then have to re-set the line weight to your prefered size.

Change the preference to keep it from happening in the future. 

First of all, you should always PLACE .AI files as a rule. Copying and Pasting is not an effective workflow.

That being said, does the same thing happen if you DO "Place" them?

Just to be sure this isn't caused by scaling, can you confirm that the two illustrations have the same overall dimensions for the art in Illustrator.

Hi,

Thanks for reaching out. Please try the suggestions shared here https://helpx.adobe.com/indesign/using/importing-files-applications.html and let us know if this helps or if you need any further assistance.

Regards

Rishabh