Your profile says you're in Minnesota. Have you recently tried moving it outside? Aloe loves sun, but after being indoors for the winter the plant needs to be gently reintroduced to direct sunlight, a few hours a day at first, then longer. Otherwise it can suffer a burn that looks a lot like those browning leaf tips.
Also, does a 1 week watering schedule allow the soil to dry out properly between waterings? Aloes are succulents native to desert climates and they are a lot easier to over-water than most houseplants.
I have 37 Aloes and they are super easy to care for. Brown tips can be caused by too much natural sunlight. While they are growing, babies are very sensitive. I have had this problem and I cut the brown tips off, not the whole leaf though. Make sure in spring you water them more because of the extra sunlight (longer days). Keep soil not dried out 100% for more than 3 days. They are in the group of succulents. Sometimes, at night I lightly mist them with purified water. It's natural for them! Desert plants are warm in the day and cold at night with moisture. Also other animals such as cats can hurt the leaves and cause the tips to change. Rubbing and chewing damages the leaves. If your plant is over 3 years of age and has less than 10-12 leaves, then sunlight may not be the cause for what I saw above.
Remember that it's your plant so do what you think best.