If you can post a picture, we could give you a better answer; also, do you know what rootstock it is on? A Meyer that size could probably support maybe 5 or 6 fruits; I wouldn't leave more than 1 on each branch; 2 if it is quite strong, or the fruit is close in to the trunk -vs- out on the end of the limb.
The thing with Meyers is they are such prolific producers that they will keep so many lemons, the tree will "forget" to grow. Each year, as the tree gets bigger, you can leave more fruit.

You should be fertilizing it 3-4 times per year with a good citrus fertilizer according to label directions. I would also give it a good foliar fertilizer sprayed on the leaves every 15 days.

my meyer was 3' tall when i bought it a few years ago the first two years it had about 10-12 fruit, as they fruit got bigger and started weighing down the branches, and then the trunk started to bend towards one side, that's when i thinned out some of the fruit. i kept the green lemons and used them to flavor my ice water and iced tea.

your tree is limber, but if you feel there's too many fruits on one branch and its bending more then you feel comfortable with, feel free to pick a few to lighten the load.

as far as whether your tree has enough energy to support that many fruit, don't worry, if it can't it'll drop a few of them. from the time it blooms to the time the fruits mature, there's usually 2-3 phases of natural fruit drop so not to overburden the tree.