If you have sleepiness arising in the meditation then it is quite important to use body awareness. If you are trying to watch the breathing it's a very fine and subtle object, and when sleepiness is present, the mind has become too dull.
Watching the breathing with sleepiness in the minds is a bit like a person lost in a forest in a fog, trying to find out of the forest by recognizing small pebbles on the ground. But if they bring the attention to a huge boulder, then it is much easier to find their way out of the forest. In meditation, that boulder is your body.
If sleepiness arises in meditation, change the object of your meditation to awareness of the body. Run your attention through the body. Feel the heaviness of the eyes, note this "heavy, heavy". Perhaps the head is tilted, feel it, allow the mindfulness to arise, then mindfully straighten it. Perhaps the back is slouched, feel it, allow the mindfulness to arise, note it, and then straighten it. Perhaps you have gone even to the stage where you are swaying. Okay, hold it, feel the body in this position, note, "swaying, swaying", then mindfully straighten it. Keep running your attention from the head to the feet, and the feet to the head, and try not to bring up aversion towards the heaviness of the body.
If you're still having difficulties, open your eyes, look down in front of you, about one meter, don't try to see any pattern on the carpet or, if there's anybody else in front of you, the patterns on their shirt, etc. Try to bring your awareness to your whole body sitting and note, "sitting, sitting". Then take your awareness to a smaller area, perhaps the hand touching, note "touching, touching", then broaden out your awareness to the whole body, feeling the whole body sitting, noting "sitting, sitting", then bringing your attention to a smaller area, perhaps the buttocks touching the pillow or the mat and note "touching, touching". What this does is break up the moments of sleepiness with moments of mindfulness, which has an energizing quality, and you may find, if you persevere that the sleepiness can actually pass and be followed with a brighter mind.
Dealing with sleepiness is quite important in the meditation because this is often the first hindrance you're going to meet when you try to practice meditation. Most of the time we are going around doing things, and when we finally sit down we think, "Ah, time to sleep". But just because we are not doing something "exciting" doesn't mean it's time for sleeping. So we have to learn how to bring the awareness to our body and break up the moments of our sleepy state of mind with a moment of mindfulness. Body awareness is very good to work with this hindrance.
Another thing which you can also do is change your posture. Standing meditation! It's very hard to be sleepy when you're standing, otherwise you fall down. So standing meditation is very helpful and also walking meditation. Do a few minutes, or longer as time permits, of walking meditation to increase your body awareness before you sit down. So if you are a very active person and you fall asleep straight away, beginning with walking meditation before you sit is very helpful to wind down but increase awareness.