Right now you should start applications of Trichogramma wasps which are used to control pecan casebearers. they are gnat-like parasitic wasps that attack over 200 types of worm pests. The wasp eggs are available in "cards" which you hang in the pecan tree where they hatch and do their thing. They are available at most organic nurseries or on line. By the way, these little guys do not bother humans and they also control web worms.

What you've described are nuts damaged by pecan weevils. A spraying program may be necessary - or installation of Circle weevil traps all the way around the trunk may be helpful in diminishing the level of infestation.

Here is a link that might be useful: Managing pecan pests & diseases

lucky_p is correct. They are hard to control without a few treatments with an airblast sprayer in August or September.

These weevils live in the ground for two years, emerge in late summer (usually after a good rain) and then hang around in the tree for a week or so before laying eggs in the nuts. It then takes about 42 days or so on average for the new weevils to consume the nuts and start coming out of the shells via the holes, and then going into the ground for another two years.

Starting by Aug 1, your best bet is to (1) keep the grass cut short around the tree (so more adults will fly or walk to lower trunk to climb rather than fly to the canopy), (2) get enough circle traps to fully encircle the trunk as high as you can while still being able to reach them, (3) check the traps daily so you know when and how many appear; keep some records of the numbers if you want before killing them, (4) try to get any nearby neighbors to do the same thing, and (5) try to get the nuts out of the tree and off the ground as early as possible when mature (when the shucks open) so that the weevils will not be able to tunnel out and get back into the ground to repeat the cycle two years later.

Short of using Sevin or similar in big sprayer (like they do commercially), this is your best bet. You can likely cut the number in half or more if you do this, but you will still have some.

The circle traps cost between 15 and 20 dollars to buy.