Is it possible to get rid of watery eyes?

Usually yes: It is important to discover the reason for the wateriness: is it allergy, chronic irritation, dry eye (!), tear duct blockage or other problem. Once this is clear then treatment can be started - usually, this is very effective.

Yes: Determine if reflexive tearing (thus treat the etiology, remove inciting factor or improve the tear film or make more tears), or obstruction of the tear drain (thus re-open it or bypass it), or any underlying primary or secondary cause. Excessive tearing is usually when you have to carry a tissue box and the tears are always spilling over like crying.