I've given Weebly a lot of hate over the past few years. Some of it is warranted, but some of it is not. After working with it a lot more I've decided that Weebly SEO is possible, and having a Weebly website can be a good starting point for a lot of businesses.
That being said, Wordpress is my go to solution for almost any website. It is extremely flexible, probably already has a solution for your business needs and has a lot of support to get things done. Wordpress also has the flexibility to completely customize it for yourself. You can hire a Wordpress developer to create a plugin to do something completely new. This isn't something you can do in Weebly. You get what you get with Weebly, which is quite a bit.
So, which should you use? It depends on your immediate budget. If you can afford a custom website design, $5,000-10,000, then go with Wordpress. If you can't, then go with Weebly. It will hold up well as your business grows.