Tiling over rolled roof
"Can I install tile over this material..."


No, not without further treatment. Composition/asphalt/rolled roofing materials are not an appropriate substrate for tile


"do i need hardy board. Would that be an ok solution to my ponding issue?"


No, Hardiboard alone will not work and will not solve your ponding issue, the water will continue to pond under the cement board


"Is additional weight a problem in the future?"


Weight might be a problem now and in the future, but weight as it relates to deflection is likely to be your biggest concern


I am afraid that you may be in for a bigger project than you envision if this is to be done properly. Rolled roofing materials are not an appropriate surface for walking on regularly, and ponding should not occur on an exterior deck surface designed for walking as they should always be sloped to drain or to a drain. It leads me to be suspicious of the original design and install.

To do it right would mean ensuring the deck is sloped to drain and meets minimum deflection specs (in other words, when a live load -person(s)- is/are on it, it does not flex too much). Then you will need to completely waterproof it (not just water resistant which is what rolled roofing is, water proof).

Down and dirty: install appropriate perimeter flashing, float concrete or "dry pack" over the existing surface to provide a slope and eliminate ponding, asphalt hot-mop (or apply some alternative high-tech waterproofer), float more concrete on that, then tile.

If it was me I would cut the deck off flush to the house and let it drop into the street, it's just a ledge for water to collect and cause damage (sorry to be pessimistic, but that's how I feel about balconies).