The upright/comfort style of the bike will have a far larger impact than weight, I would venture.
The more upright the bike, the more you're 'sitting' on the saddle instead of distributing your weight between saddle, pedals and handlebars. The more leaned over/'aggressive' positions are *much* more comfortable for people who ride regularly, and have developed the muscles for it.
If you ride several times a week for more than an hour, you will likely be happier with a more leaned over riding position. The multiple hand positions available with drop bars are another major factor.
If you ride only occasionally, tend to 'cruise' instead of riding quickly, or have any back or neck issues which preclude the more leaned over posture that a normal road bike dictates, a comfort style bike will be the ticket for you. Assuming it fits reasonably well, and the saddles agree with you, comfort bikes are fine for an hour at a time or so. Just don't expect that you'll be comfortable sitting on a big cushy bike seat for 6 hours just because it's called a 'comfort bike'.
When pricing out bikes, something to consider is the used market. $800-$1000 can get you a decent quality and condition used bike in the somewhere around 10 year old vintage. Anything newer than early 90s will be more likely to have standard parts which are still available, also often allowing some carefully selected upgrades to things like the drivetrain, brakes, wheels etc if the opportunity presents itself, or it becomes necessary due to worn out older components.
If you're comfortable wrenching on your own bike, or at least are familiar enough with the technology to evaluate the quality and condition of an older bike, used is definitely the way to go in your price range. If you can cultivate the help of a bike savvy friend who you trust, especially one with tandem experience, buying used can be a good idea even for someone new to the game. I know *I* certainly enjoy helping get friends onto bikes they'll enjoy, it's like shopping with other people's money.
All that being said, even 'low to middle' range bikes (anything above the 'department store' level) these days are pretty serviceable. The Tandemania Sport has several features which put it head and shoulders above the ultra-cheap tandems out there, and even above many older inexpensive tandems. It's got an eccentric bottom bracket for chain tensioning, middle of the road derailleur system (Deore), and linear pull brakes.
If you can hunt for a deal on a Tandemania Alite you might be able to find one for not much more than the MSRP on the Sport. Then again, you might be able to find a Sport out there for less than $800, too.