Is it better to wear a slightly weaker or a stronger eye prescription?

My optometrist is giving me the option of changing my glasses lens to either a "perfect" vision prescription (-4.00 in one eye and -3.75 in the other) but this seems to make me feel dizzy when I look at closer objects. Otherwise, she said she can give me a slightly weaker prescription that will be easier for me to get used to (-3.75 in one eye and -3.5 in the other) but this is not as clear when looking at objects at a distance. My question is this: Is it better for your eyes to wear a weaker prescription or a stronger prescription? If I wear a weaker prescription, will my eyes get tired and eventually get worse? If I wear a stronger prescription, will my eyes get weaker bec they are not "exercising" and also get worse? My optometrist said it was up to me but I just want whats best for my eyes in the long term!

My sight had not changed for years until a recent job change where I spend +9 hours a day on the computer - can they get better if I take more breaks and exercise them more?

Ask your optometrist for a mid range prescription, sometimes called computer glasses. The focal range for this is 30-36 inches instead of the 18 they use for reading.
It is best for your eyes to wear the correct prescription, neither weaker or stronger, the only practical exception for this is if you have never worn glasses and have always needed a strong prescription, then it might be hard to get used to.
It sounds like what has happened to you is you need one prescription for distances, like driving, walking, watching TV.
And a different prescription for reading, and now that you spend so much time in front of a computer, you need those mid-range glasses.
Your vision is relevant to the shape of your eyeballs, your eyeballs don't exercise, the muscles that control them do and you will do nothing more than tire them if you constantly make them work to do something they cannot do.
They will not get better, they will not get worse. You will become more aware of how you see if you don't wear glasses, but it will not change the problem.
In the long term, get a pair to keep at the computer.
Get one to read with,
Get one to drive with.
I know its a pain, but I think you and your eyes will be happier in the long run.

Your eyes won't get worse from wearing a weaker presciption nor will they get worse from wearing the stronger one (sorry for not making your choice easy) Just ask yourself a question.

1) Do I need absoutley perfect vision in the distance? and if yes...are you prepared to put up with feeling dizzy for a little while when you adjust...which you probably will.

Getting a slightly weaker prescription will probably reduce the chances of your eyes becoming fatigued and giving you headaches and whatnot.
That's why my doc told me at least because we couldn't really get my right eye "perfect."