If he is really wanting to compete, there may be a way to do that and reward yourselves for doing a good job without the competition revolving around pounds on the scale.
Explain to him that losing pound weight is usually quicker and easier for men than it is for women, and that if he wants to compete with you-that the competition be revolved around fitness and personal habits rather than scale weight.
You could set up a little chart, and each set certain goals for the week-such as getting in 8-10 cups of water a day, each of you not having any unhealthy food binges, or something fitness related-such as walking 2 miles every day. Your goals may be different because of your gender and fitness level-but the competitive points should be similar. You could each get a check or star each day for getting your goal exercise in-for you it may be walking 2 miles a day, and for him it may be biking 5 miles or something-but similar.
Rather than competing on the scale, you could compete on how many goals you met each week. Say you got in all your water, met your exercise goals each day-so you have 14 "points".

He missed a water goal one day, so he has 13. It makes competition more for the healthy habits-not the scale results.