Hey Curl
4% looks strongly like QQ+ and AK.
He checks the Qd. So he is afraid of a flush or inducing a bet on your side because he has the nuts.He might also be afraid that you have AJs or AQs which now got there and beat his AK. Broadway flushes are not possible any more, and something like 87d to T9d that might ocassionally call a 3b IP fold the flop or the turn the latest because you did not get the odds.
after about 15 minutes of thinking about this hand I am pretty sure that he is waighted towards AK. The majority of these combos will fold to a shove on the river. Maybe AK with one diamond will call after a AI as it would be a decend bluff catcher, but the only hand he will always call is AdKd as well as AA and QQ as it is oooo unlikley that you have any flush here. So I guess that shoving here might be - EV .I think raising the turn would be clear +ev as lots of AK will call expecially because the 2nd diamond looks so much like a semi bluff with a floating 87-T9d.
The second reason why i want to raise the turn is that you are afraid of any Diamond or K or Q. (and if he 3bets wider a 10) Maybe this is not line with the highest +EV on the long run but i hate to be in a tough spot if one of those cards shows up.
Disclaimer: I am a starting player and want to improve my game by contributing to threads like this. I am by no means a poker expert. So I am as much interested in your feedback to my thought process than you might be in my answer. I hope it helps and wish you good luck - also english is my second language
