Is a 600cc silicone moderate profile gummy bear implant under the muscle going to cause significant stretching of skin? (Photo)

I do not think that it is helpful to classify breast implants as "big"...  these types of classifications are not helpful given that everything depends on the patient's anatomic starting point and goals.     
In other words, it is not necessarily that a specific breast implant implants is "big" or problematic;  it is that the use of a breast implant that is TOO  large for a patient's frame can be problematic.  
The use of a larger breast implant (than what is safely "allowed" by the patient's anatomy) can be problematic;  potential problems include breast implant displacement/malpostion issues ( such as bottoming out, lateral displacement, symmastia...)  and/or significant breast implant rippling/palpability.
Keep in mind also that there are many variables that come into play when determining the specific aesthetic outcome achieved with breast augmentation surgery.  The patient's starting point, for example will determine to a great degree what can be achieved but surgical maneuvers can also play a significant role.  Exactly how/where the breast implant "pocket" is dissected and which breast implant size/profile is selected will play a big role when it comes to final aesthetic outcome achieved.
 My best suggestion: select your plastic surgeon carefully. Make sure that he/she is a board-certified plastic surgeon who can demonstrate significant experience achieving the types of outcomes you would be pleased with. Then, communicate your goals carefully as well.  The use of goal photographs and computer image may be very helpful during the communication process.  Remember that terms such as "D or DD cup" may mean different things to different people; best to avoid the use of cup sizes as a reference point. After doing so, your plastic surgeon will be able to tell you whether or not the desired outcome is realistic (or what you should realistically expect), given your specific anatomic starting point.
 Best wishes.

It's hard to recommend an implant size without examining you in person.  Every doctor uses his/her own way to choose a size for patients.  I would recommend going over sizing with your plastic surgeon if you're not quite sure about the perfect size for you.  

Tall women with larger frames and broader chest, shoulders, and hips can often handle larger implants that would make smaller women's chests look overcrowded and heavier.  I would recommend that you go with the size that boosts your self-esteem, and fits your anatomy.  Implants of 600cc and higher will create more tissue thinning over time, have more potential for rippling, more potential for bottoming out, greater likelihood of breast lift revisions, etc. 
Kenneth Hughes, MD, ABPS Board Certified Plastic Surgeon
Los Angeles, CA