There are two ways to log your weight:
You can log weight for any date — just include the date in your message, like "weight 163 on Monday".
Your weight appears in your fitness summary and is used to calculate your power-to-weight ratio (watts per kilogram or watts per pound). This is one of the most useful numbers in cycling — it tells you how much power you produce relative to what you're carrying up hills.
Ask "what's my weight?" or "show my weight trend" to see your weight history.