Cinnamonroll
Your bill likely increased due to either a plan or special discount ending. You can view your invoices on the HughesNet MyAccount site to see exactly what the charges are and compare your current invoice to the prior one. The invoices are on the "My Bill" tab. While looking at an invoice, which will be in a popup window, you can scroll down and click on the blue entries to see their full breakdown.
As for changing your plan, the prorated charges will be on your next bill. HughesNet uses forward billing, meaning when the invoice is created and charged the charge is for the new month, not the month you just finished. i.e. if the bill is created and paid for on December 5th, it's for service from Dec 5th through Jan5th (actually Jan 4th at 11:59:59PM). When you change plans, the remainder of the month for the original plan will be credited and the remainder of the month for the new plan will be billed, and this difference will be reflected and included on your next bill.
As for the actual plan change, you can call 866-347-3292 or do it online. If you sign into the same HughesNet MyAccount site, hover over the Shop/Upgrade header and click on the Plans & Pricing tab, you can see the other plans available to you. When you click on "Click here for pricing", it will show you the price and give you the option to change your plan there. If you add it to your cart, it will show in the shopping cart on the upper right. When you click on that cart you'll be able to see what to click on to complete the order.
Hope this helps. :)