Perfect "have" coupled with progressive/continuous "been enjoying", expresses a present or recent ongoing action/state; e.g., I have been enjoying our visits together.
What our sentence needs is a perfect verb + a gerund, either stated or implied (. . .), and maybe even add in "ever" to give it a bit of extra continuity:
EX: I've enjoyed [playing] sports ever since I was 3 years old.
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