It is very normal for a pup not to sleep through the night at 16 weeks. For one, they can't hold their potty all night yet. Their organs are just not big enough. We had to get up with Rylie to let her go potty during the night for quite awhile.
It is good that he is barking to let you know he has to go and not just going in his crate.
Welcome to puppy parenthood, which is filled with getting up in the wee hours
He'll get old enough to hold it all night eventually and stop waking you up. Rylie just stopped barking to go in the middle of the night one day.
Note: Make sure you only take him to do his business and do not do anything else with him when he gets up. That way, he knows the only time he gets out of the crate in the middle of the night for making noise is to go potty. If you do anything else with him (e.g. play, feed, just bring him up for attention, etc.), it may encourage him to whine/beg to be let out. So if he wakes you take him straight to potty (if he doesn't go that's fine) and then straight back in the crate to sleeping.
I hope this helped some. It was also a bump in hopes that others will have some advice too. Welcome to YT!