Extremely clingy 3 year old

My DS turned 3 in March and since he was about 2 and a half, he became very clingy to me, to an extreme. I mean, I am the only one that can do things for him, like get him whatever he wants, take him to the toilet, do his seat belt on in the car, turn on his DVD, I mean ANYTHING. Even taking him to cc, I have to do it, no one else can. He used to go to cc and go and play with no problems when I left, now he is terrified when I leave him, clinging to my leg and watching me like a hawk to make sure I stay. This leads to me staying for a good 30 minutes, with me sneaking out eventually. He constantly says 'mummy do it', even when I ask if daddy or nanny or whoever is there can 'do it'. It's gotten to a point that I am so tired all the time of being wanted 24/7. Even when he goes onto a trampoline, I have to either go on it as well, or I have to watch him, no one else can watch him. Or they can, but I have to be there as well. When he wakes up in the middle of the night he calls for mummy, never 'daddy'. Is this normal 3 year old behaviour? He's never been a clingy baby, though at some point he fretted when I left the room, but it only lasted for a while. My OH started working in our business 6 weeks ago, which means he's gone all day and I initially thought he's wanting me because I am the primary caregiver. But this behaviour started way before OH started working (he was previously at home with us 24/7). And ideas or comments or advice?

TIA.

Both of my boys have been like this, DS2 (who was 3 in April) is still very much in this phase, everything is about me. Sometimes it's cute, like this morning when he told me that I was his best friend :) Sometimes it's not so cute, like I really don't need an audience every time I have to go to the loo. DS1 (nearly 6) still has his moments, but he's much more balanced these days, although I couldn't tell you when it started to change, partly because it's so gradual & partly because I'm the one who is there the most to do things anyway.

I think being 3 is a pretty full-on time, they're so ready to be "big", but they need the security of being looked after because they're actually still pretty little. It's exhausting to be the one they want all the time, but for me it's the continuation of gentle, attachment style parenting - full on while you're in the middle of it, but great pay-off as they come through it.

Thanks for your reply Bhoysgirl. I think that's what it is, he's growing up and realising it, but is too scared to let go of me and all the security.