Look at the weave first
Loose, worn or very fine cloth may not have enough structure to hold a heavy thread under tension. Test a spare area and inspect whether the holes are widening around every stitch.
A backing layer or patch can distribute the load, especially for a repair. Do not rely on tighter pulling to make a weak cloth behave like a stable one.
Balance needle and thread
A large needle can leave a hole that the thread does not fill, while a thick thread may force the weave apart as it passes. Try a smaller needle or finer thread on a sample.
The needle should carry the thread cleanly without creating a noticeably oversized path. Compare front and reverse stitches rather than judging only by the line on top.
Use moderate tension
Pull until the stitch lies flat, then stop. Excess tension can draw the thread back through a loose weave and create puckering at the same time.
If the fabric remains weak, widen the repair area and reduce stitch density. Support should come from spreading stress, not from forcing more thread into the same fragile holes.