3 inches tall is ok for a 6 week old seedling; most seedlings of modern roses begin to produce blooms at this stage.
Are your seedlings growing under fluorescent light???
dave wolfe

the seedlings just look so weak and thin. I don't have any lights set up on them. its possible that they just need more light. There are no signs of any blooms in the near future.

Best to put seedlings under fluorescent light, keeping leaves as close to bulbs as possible.
At this time of year, there is plenty of sunlight outside, but the seedlings may be too fragile to adjust to it; when my seedlings first go outside, they are covered with translucent plastic for a couple of weeks while they get used to sun; good ventilation is essential to prevent overheating.

I just got the first few rose seedlings sprouting in my refrigerator too. ^_^

Just as a general comment, besides light, being planted too close to other plants or in too small of a container can also slow seedling growth. So can being kept in a room which is too cold, plant metabolism is strongly linked to temperature.

currently the roses are in 4-inch pots and I think this is sufficient for now. I made a mini greenhouse and the roses seem to be doing better. most of them have a 5 leaf set and are growing faster. they still seem so thin compared to all my other roses. when does the stalk begin to thicken?

My largest seedling is about 5 inches tall, the stems still look thin. *shrug* They seem happier since I added a second fluorescent light fixture over their shelf though. This reminds me I should look through the seeds in the fridge to see if any more sprouted. So far none of the tea rose seeds have sprouted, only the rugosa seeds.