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Heavy horse leans on bit does not give

hi all I have been having heaviness issues with the horse I lease ( I have access to do anything I want with him) he is a 16 year old dressage horse was told he has shown second level (no idea how with the lack of give) I have took the last year to “play” trial and error.

First I started going back to the ground and just did ground work and suppling exercises (he did wonderful) he does great in side reins lifts his back and gives to the bit.
then started riding again, rode super soft give him big realesses and praise at the littlest of gives as if he was a green horse. Slowly started to ask for a little more and litttle more he was still doing pretty well until we got to what I would consider a training level frame then the pulling unwillingness to give fighting started back up. Just like it was 5/6 months prior
Then I went to tack (both my saddles have been fitted to him and checked regularly) so I started changing bits he would go great in anything new for the first 3/5 rides then right back to the pulling. I had also tried the micklem bridle did wonderful for first couple ride right back to normal. Most bits I have used are dressage legal I tried a hackabit just to try and the same thing happen even with the long shank
I have been taking lessons on a school master to help me learn to ride him better, I try to apply what I’m learning to him it still doesn’t help much
as soon as I pick up to ask for for he just put his head up and avoids giving tothe bit. I know he was trained in heavy hands in the past and used side reins so I know that is working against me!
all health pain issues have been looked at he gets his teeth done every 6 moths and sees the vet every 4 month

any help would be greatly appreciated. Weather it be training, different tack any suggestions!
Thank you!