Will a 7.5 mm chin implant (horizontal projection) cause a deep fold between my chin and lip? (Photo)

By definition any form of chin augmentation, by an implant or moving the chin bone, will make the labiomental fold deeper. This is unavoidable as the fold represents a fixed anatomic point that is influenced by changing the chin projection below it.

The side profile photograph demonstrates a significant weak and recessive chin profile for which a chin implant can improve.  Chin implants are not designed to augment the groove between the chin and the lip.  Chin implants are manufactured in a large array of sizes, thicknesses, and shapes which is best determined at the time of the consultation and examination.  For many before and after chin implant examples, please see the link and the video below

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  From the photo, your chin is very weak.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.    There are numerous shapes and sizes of silastic chin implants, some of which are rather old shapes that do not yield the desired "natural" aesthetic results.  The Curvilinear shape is an example that is similar to the old "button" implants (had no wings or lateral tapering elements of the newer EAC design) that created a "pharaoh" shaped chin.  The EAC or extended anatomical chin implant style offers, in my experience and humble opinion, the most natural, aesthetic result when augmenting the chin.  The EAC in a size small is the most common implants that I use in women ( size medium in men ).  Proper placement and the appropriate approach (placing the incision under the chin and not inside the mouth) are also key to obtaining the best aesthetic result.  Using an implant with 7.5 mm's of projection would equate to a size Extra Large implant.  This increases the front face as well as thickness of the sides (wings).  Wide wings are more likely to impinge on the mental nerve and create stability issues due to the thickness of the implant.  In my experience it's best to place the most appropriately sized implant that can be placed without increased unwanted side effects.  
Hope this helps.