Looks like you have a very young tree that is responding to growing conditions in a small container; variable sun/shade, moisture, and nutrients. Avocado trees require years before fruit production begins, so you should prepare for the long term (5-7 years) with patience, and it is good you started with a grafted plant. It will have to be moved into larger containers with ample drainage as it grows; don't let it become root bound. Leaves turning brown at their tips may indicate too much water or wet feet. Also, have precautions in your Zone 7a winters, as freezing temperatures may affect your little Avocado, which would prefer at least a subtropical climate - recommended for Zones 9b-11. For more info, Google search "avocado (Persea americana)" but you won't be looking for Guacamole recipes yet. :)

I remembered subsequent to posting that I had the same problem last year with another avocado tree. Same discoloration and drying out. I had applied little/no fertilizer for the duration of its life if I recall correctly, yet it had the same problem. Even still, I will withhold fertilizer, as RodneyJS suggested, to see if it helps at all. The internet seems to suggest avocados will tolerate full sun. It's definitely getting sun from morning to night in its location, including strong afternoon sun. I am going to try, despite its preference for full sun, to move it to a spot where it gets sun in the morning and midday and partial shade in the afternoon. Will this help? Also, as you can see from the picture, it is on a black asphalt roof that gets very hot (too hot to walk on barefoot on a sunny day). Could it be getting too hot? Again, all my citrus trees seem to be happy as ever with all of the same conditions and care, but I'm just wondering.

Looks like several issues; an apparent deficiency of Mg and Mn, which can be compounded by a high pH soil and/or cool weather. The brown leaf tips are an indication of salt toxicity, which can be partly solved by a good flushing of the soil. Your new growth appears to be better; so these issues could now be only history. If your soil pH is over 7.5, it might be a good idea to add some soil sulfur to lower it; and sulfur is good for most citrus.

The trees were removed from the soil, where they had been happy and flourishing for a couple years, put in large pots for around month, where they stayed happy and lush, while the soil level was lowered by a few inches and leveled. Then a couple inches of compost was tilled in, and the trees were put back in their same spots. They're planted on slight mounds. They were put back in the ground the exact same way as they had been before, basically just put them in. The first time I planted them the top few inches of soil were amended with special citrus soil from home depot about 5 feet in all directions from the trunk. I didn't amend them after transplant because the compost was tilled in. The compost was redwood and manure, and everything else seems happy in it. I have lots of stone fruit trees as well and none of those have had any problems with transplanting, just the citrus. The injury to these trees came basically immediately after transplant. I used the urine mostly on that lemon and the results were great, it was much yellower before! The other trees get it sometimes but not much and not regularly. Urine was applied only after these symptoms had been present for about a month. I quit when I got tired of collecting it. Glad to hear the potted kumquat is ok! I have a ph meter but I think it's broken. I'll definitely check the ph!! If it is alkaline, how do I fix that? I think it's strange that they would be so unhappy when they are in virtually the same soil, in the same spots that they previously flourished!