Will Weight Loss and Gain After Neck Lipo Affect the Results?

Significant weight fluctuations after body contouring procedures will "undo" the results. Even if you have not had surgery, weight fluctuations makes skin "age" faster, as the repeated stretching of the dermis damages elastic fibers, and results in less elastic skin. Skin naturally looses elastic properties as you age, so any process that speeds up this occurrence makes you seem to age faster. The main examples are: smoking, sun exposure, and major weight fluctuations.
10 lbs is not a significant amount of weight for most normal sized individuals, so this is a bit of a theoretical discussion. (But if you want to know the details, then yes, it does effect the results.)
Dr.B

Thank you for your question. You may find with small degrees of weight
fluctuation (e.g 5 lbs), your chin liposuction results do not change
much. With larger degrees of weight fluctuation (e.g 20 lbs), your
results will likely change. You still have fat underneath the platysmal
muscle. If this reduces considerably with weight loss, then you may
find you start to develop a hollowness under your chin. Likewise, you
may find that with large weight gain, that your fullness is returning.
As with other body parts, the stability of the result does follow weight
changes.

Great question! Fluctuations in your weight may result in sagging of the skin and negate the result or leave you with a different problem, namely, the excess skin which is more difficult to correct. Some patients are more sensitive to weight fluctuations than others.