How will becoming obese affect my relationship?

Many reasons. Aside from the physical appearance, obesity can adversely affect your health by increase your risk of developing cardiovascular disease, diabetes, stroke, metabolic disease, cancer...It can also affect your mood, energy level. If you are obese during pregnancy, your unborn child has a higher risk of obesity as well...
Relationship. It's hard to say. It may or may not affect your relationship. What is known is that divorce rates are higher in obese people that have lost a lot of weight. So, i tell all my weight loss surgery patients that so they know what to expect. When two people are overweight and one becomes thin, it can put a strain on a relationship.