Why does my eyeball ( right eye) look bigger than the left eye ?

Eye asymmetry could be due to eyeball position asymmetry or eyelid asymmetry. Need consultation with an oculoplastic specialist to determine the cause of the eye asymmetry which would determine possible treatment.

Please consider post your question with a photograph. Without that information, it is really hard to say much more than, see an oculofacial surgeon for a personal assessment.  The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains a regional directory on their website that can help you find a highly qualified surgeon close to home.

I have no idea what is going on based on your description, but it does tell me that you need to be evaluated by an oculoplastic surgeon.  They should be able to evaluate the complaints related to the relative sizes and positions of your eyes.  Good luck! 

Hello OscarpinedaFSH3It is very hard to give sound advise without pictures. However, bulging eyes can be caused by many different factors.  You may need imaging tests first to get a picture of the orbits. Seek out an expert Oculoplastic surgeon to have this discussion.Cheers 

Lazy eye means so many things. To some in means an eye that can't see as well as the other, as you describe. To others it means an eye that is not aligned with the other. To others it means a droopy lid.
The first thing to address is the vision. If your eye have a tendency to wander then blur from any cause would make that worse. 
If the vision is fixed, then alignment can be addressed if necessary.
Finally the lid position, would be the last thing to address as it can change with the earlier treatments.