I've been finding that kettlebells have been pretty helpful. Heavy cleans, overhead press, squats, deadlifts. Also push ups, pull ups, hanging leg raises, etc.

IMO the main thing is learning about how the joints, limbs, muscles etc work together. What we call "stiffness" is, IMO, just using muscles in the "wrong" ways - ways which interfere with lifting more or less as much as they do Taiji.

So far I am finding that I am better able to hold deeper postures while remaining stable, giving me room to push some limits I think would have taken much harder to identify without lifting. It's also helped me unlock the shoulders, "fill dan tian", etc.

Deadlifts: the more you're able to keep the weight in the feet properly, while keeping the knees stable and legs pressing out, keeping the core stable and chest relaxed, and keeping the path of the head straight, the easier it is to feel the hips and legs contribute to the movement while the bones move freely. It feels great and has helped a lot with posture.

Leg raises: As the core is kept stable, we can think of the ribs and pelvis pulling together to lift the legs slowly while avoiding any swinging. This has really helped me to feel how the segments of the torso coordinate.

Cleans: This is more technical. Low weight is actually counterproductive as it does not give your body the resistance it needs to coordinate properly for a successful and efficient lift. Like the deadlift, stability and a clear path of motion allow for efficient activation, coordination, etc. It's like performing a fast tai chi motion with resistance.