Check to see that the key isn't catching on anything obvious - if any part of the key is contacting another key along its length it'll cause that hesitancy.
Have a careful look at the key lever arm down by the Auxilary F key - make sure the lever isn't catching anywhere down there, and look for any bits of cork or packing material that may have got caught in the keywork.
Operate the key and watch what the spring does in its cradle (the little bit of metal that hangs down off the key, where the end of the spring sits), sometimes you get a small catch there. Try popping a tiny drop of oil onto the spring cradle
I'm assuming it only catches when you're playing a Bb. If not, check that the BisBb key pearl isn't catching on the B key cup.
Look underneath the A key pearl, check there's nothing caught on the felt/cork.
If none of that shows up a reason then there's a chance that there's a problem with the point screws - or perhaps some binding of the key barrel against the pillars.
If you feel confident enought you could try giving the screws a turn.
Start with the top one - and before you start make a note of the alignment of the screw slot...you may need to return the screw to this position later.
Strart by undoing the screw half a turn. Check the action of the key - if no different give it another half turn and check again. If no different do the screw up again and try the same with the lower screw.
If there is a difference, leave the screw where the key works best - but check that there's no play in the key from side to side (grip the key barrel just before the pillar and give it a wiggle).
If none of that works, try to grip the lower pillar with your fingers and pull the pillar back. Don't go mad, just apply a firm and steady pull - and then try the key while maintaining the pull on the pillar. If that works then the key barrel needs shortening a tad.
You could try it with the upper pillar, but there's less access to it. You might just be able to get a finger on the top of the pillar to push it away.
Does the key have a guide? This will be a cutaway pillar somewhere along the length of the key barrel (your G key will probably have one). These are a common cause of binding if the padding material fitted to them is too bulky.
A short-term fix might be to increase the tension on the spring. This will hide the problem for now, and it might just go away of its own accord...or you could take it to a repairer and have it looked at. It'll be something simple.
Regards,