The brown leaves are probably because of sun. For the smallest leaves do you refer to the outmost leaves or innermost leaves? When Aloe vera is short of water, their outer leaves will become thin and curved inward first. There can be 2 reasons for Aloe vera being short of water - either underwatered or overwatered. For underwater, just water it more. If the latter, it probably got rotted roots which makes the water in the pot unavailable to the plant. May I ask you what kind of soil or mix you put it in? If that's gritty mix or alike, it's not likely to be overwatered. In case you just put it in potting soil or even Cactus soil, you got to check if the soil is still wet inside. You can push a skewer down into your pot till its tip is closer to the pot bottom, wait a minute and pull it out to see if there's a lot moisture on the skewer. If it looks very damp or to the touch, you potting mix probably is not very fast draining. Got to make some change then.

Naughty poster I am, life got busy and I was never able to follow up on this... The pots with grit are indeed a pure 50:50 grit:clay mix, essentially the famed "Gritty Mix" sans bark. Other mediums are a hodge podge; some are in fresh potting mix, others in old used potting mix, fine mix, chunky bark mix, or aquarium rocks occasionally flushed with water, clay sans grit, garden soil, etc. Watering for most is via the bottom, a few minutes in a tray of aged water, then set on a grate to drain; monthly-ish or whenever the leaves start to look thin; medium at that point is nearly bone dry. No standing water; the ones in a soiless medium are flushed with water. Yes there are cats, but I've intentionally kept a group of the aloe pots out of reach to rule that out as a cause, and the spots continue to develop... So unless they're three-month delayed bruises? I've now separated the ones with spots from the ones without, as a precaution, in case is it caused by some sort of communicable pathogen, and am being extra stingy on the watering. Nothing I can find online seems similar... The closest is "rust" but I don't have the red color or open wound lesions. I'm stumped.

Any chance you had splashed water in the crown? I don't see any mushy leaves, or does it just not show up well in the pictures? The darker area on the leave that is bending, is that mushy? Try to give the plant optimal (as close to it as your place allows) of bright light ( in general any plant that has not been in direct sun light needs to acclimate to direct sunlight slowly or it will sun burn) ( I typically keep mine in a west window that gets only a brief bit of direct afternoon sun), good air circulation away from cold/hot drafts, water thoroughly then allow to dry to the level of just barely dry (not cactus/desert dry) before watering again. Average room temperature and Humidity should do. Typically if an Aloe plant is too dry it will shrivel, so I am not sure what is going on with your plant. Anything more you can tell us about the plant?

L, Aesthetics aside, they're not unhealthy as long as the plant's healthy. They eventually fall off. ETA - your plant looks in the pink of health. As stated, the overweight leaves are a case of too much water/not enough sun, air movement and higher temps. Aloe vera is thought to have come from the Horn of Africa/Arabian Peninsula area (its origin is unknown), and grows quite well under harsh conditions. My recommendation is to back off on the watering to 2-3x a month - that would allow those leaves to lose their overabundance of water.