“I've had this presentation looming over me for weeks now.”

You have an important presentation for school that's due this week. You've been thinking and worrying about the presentation for three weeks. You say this while talking to your boyfriend about the pending presentation.

I've had this presentation looming over me for weeks now.

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this (thing)

In the example above, the speaker says "this presentation". Using "this" makes it seem like the speaker wants to continue talking about the presentation.

(someone) has had (something) looming over (them)

When something "looms" over you, it means that it's floating or hanging ominously. It feels threatening and makes you worry that something bad is going to happen. The best example of this is when dark clouds are floating in the sky. You can describe it this way if you write a story about a scene:

There were dark clouds looming overhead.

People also use "looming over" to talk about a bad event that they know is going to happen in the future:

My 40th birthday is looming right around the corner. I'm not looking forward to that!

for (length of time) now

You can use the phrase "for weeks now", "for two days now", "for 5 years now", and so on. When you use the word "now" after a length of time, it shows that you think this was a pretty long time. Not a really long time, but maybe longer than you expected. For example, if you're telling someone how long you've been studying English:

I've been studying it seriously for over three years now, but there are still little things that trip me up.