29 yr female. Best option for weak jaw/recessive chin? (Photo)

From your photos, it appears your profile would be improved with neck liposuction and chin implant.  Both procedures can be performed at the same time, and a very complementary to each other.  Liposuction will help to slim the neck silhouette, while an extended anatomic chin implant will help to provide better chin projection.  These procedures can typically be performed under local anesthesia with mild oral relaxing medication.  I suggest an in person consultation with a surgeon specializing in facial cosmetic surgery.  Good Luck!

Based on your photos, it does appear that you would be a good candidate for chin augmentation with an implant.  It also appears that liposuction under your chin (in the upper neck) would help to balance your profile.  Both of these procedures would most likely give you the best result.  

You are not AT ALL a case for liposuction at the neck, absolutely not. All the patients with weak chins have
flaccid submental "hammock" due to the short distance of attachment of
the floor-of-the-mouth musculature; this flaccid submental area is
authomatically corrected after the OSSEOUS genioplasty, NEVER with chin
implants.
I perform regularly all kinds of genioplasties, not only sliding
genioplasties but also one, two and three-dimensional augmentation
and/or reduction genioplasties, plus other custom designs; in other
words, I know well what I am talking about.
You are a case for a sliding genioplasty to increase onlychin projection, or alternatively performing a two-dimensional augmentation genioplasty to increase vertically as well as anteriorly (to be discussed) your chin dimensions.
This is an awesome, lifetime lasting, stable and safe procedure, which
notwithstanding needs very accurate preoperative antropometric
planning, desing, discussion and a brilliant execution, a technique full
of creativity and good aesthetic judgement requirements.
Chin implants have many disadvantages:
-visibility, static or with facial gestures / smiliing
-artificialness, fake look, evidence of implant presence

-limited lack of versatility, they do not provice vertical modifications neither reductions
-common infections
-common dislocations
-possible nerve irritation and pain
-short lifetime
So sooner than later they are normally removed, or exchanged by an osseous genioplasty.
Why
so popular (chin implants) then? Simple answer: they are technically
accessible to all surgeons, little training is required, can be done
under local and sometimes office based procedures, they are cheap.
Osseous
geniplasties are more expensive and need good skills, true, but when
performed they produce lifetime results, safe, stable overtime, very low
rate of complications, versatile three-dimensional modifications
(augmentation or reduction, vertical, horizontal and depth), low rate of
reinterventions, etc.
Feel free to request any additional information from me.